CHRIST (Deemed to University), Bangalore

DEPARTMENT OF STATISTICS_AND _DATA_SCIENCE

School of Business and Management

Syllabus for
Master of Science (Statistics)
Academic Year  (2023)

 
1 Semester - 2023 - Batch
Course Code
Course
Type
Hours Per
Week
Credits
Marks
MST131 PROBABILITY THEORY Core Courses 5 4 100
MST132 DISTRIBUTION THEORY Core Courses 5 4 100
MST133 MATRIX THEORY AND LINEAR MODELS Core Courses 5 4 100
MST171 DESIGN AND ANALYSIS OF SAMPLE SURVEYS USING R Core Courses 6 4 100
MST172 PYTHON PROGRAMMING FOR STATISTICS Core Courses 6 4 100
2 Semester - 2023 - Batch
Course Code
Course
Type
Hours Per
Week
Credits
Marks
MST231 RESEARCH METHODOLOGY AND LATEX Core Courses 3 2 50
MST232 STATISTICAL INFERENCE I Core Courses 5 4 100
MST233 STOCHASTIC PROCESSES Core Courses 5 4 100
MST271 APPLIED REGRESSION ANALYSIS Core Courses 8 5 150
MST273A PRINCIPLES OF DATA SCIENCE AND DATABASE TECHNIQUES Discipline Specific Elective Courses 6 4 100
MST273B BIOSTATISTICS Discipline Specific Elective Courses 6 4 100
MST273C OPTIMIZATION TECHNIQUES Discipline Specific Elective Courses 6 4 100
3 Semester - 2023 - Batch
Course Code
Course
Type
Hours Per
Week
Credits
Marks
MST331 STATISTICAL INFERENCE II Core Courses 5 4 100
MST371 TIME SERIES ANALYSIS Core Courses 8 5 150
MST372 STATISTICAL MACHINE LEARNING Core Courses 6 4 100
MST373A JAVA PROGRAMMING FOR DATA SCIENCE Discipline Specific Elective Courses 5 3 100
MST373B CLINICAL TRIALS Discipline Specific Elective Courses 5 3 100
MST373C RELIABILITY ENGINEERING Discipline Specific Elective Courses 5 3 100
MST381 RESEARCH - PROBLEM IDENTIFICATION AND FORMULATION Core Courses 3 1 50
4 Semester - 2022 - Batch
Course Code
Course
Type
Hours Per
Week
Credits
Marks
MST431 SURVIVAL ANALYSIS Core Courses 5 4 100
MST432 DESIGN AND ANALYSIS OF EXPERIMENTS Core Courses 5 4 100
MST433 STOCHASTIC PROCESSES Core Courses 5 4 100
MST471A NEURAL NETWORKS AND DEEP LEARNING Discipline Specific Elective Courses 6 4 100
MST471B STATISTICAL GENETICS Discipline Specific Elective Courses 6 4 100
MST471C ACTUARIAL METHODS Discipline Specific Elective Courses 6 4 100
MST481 RESEARCH MODELING Core Courses 5 2 50
MST482 SEMINAR PRESENTATION Core Courses 3 1 50
5 Semester - 2022 - Batch
Course Code
Course
Type
Hours Per
Week
Credits
Marks
MST531 STATISTICAL QUALITY CONTROL Core Courses 5 4 100
MST532 MULTIVARIATE ANALYSIS Core Courses 5 4 100
MST571A BIG DATA ANALYTICS Discipline Specific Elective Courses 6 4 100
MST571B DEMOGRAPHY AND VITAL STATISTICS Discipline Specific Elective Courses 6 04 100
MST571C RISK MODELLING Discipline Specific Elective Courses 6 4 100
MST572A BAYESIAN STATISTICS Discipline Specific Elective Courses 6 4 100
MST572B SPATIAL STATISTICS Discipline Specific Elective Courses 6 4 100
MST572C NON-PARAMETRIC INFERENCE Discipline Specific Elective Courses 6 4 100
MST581 RESEARCH IMPLEMENTATION Core Courses 6 3 100
6 Semester - 2022 - Batch
Course Code
Course
Type
Hours Per
Week
Credits
Marks
MST681 INDUSTRY PROJECT Internship 2 10 250
MST682 RESEARCH PUBLICATION Project 0 2 50
    

    

Introduction to Program:

Master of Science in Statistics at CHRIST (Deemed to be University) offers the students an amalgam of knowledge on theoretical and applied statistics on a broader spectrum. Further, it intends to impart awareness of the importance of the conceptual framework of statistics across diversified fields and provide practical training on statistical methods for carrying out data analysis using sophisticated programming languages and statistical software such as R, Python, SPSS, EXCEL, etc. The curriculum has been designed in such a way to cater for the needs of stakeholders to get placements in industries and institutions on successful completion of the course and to provide those ample skills and opportunities to meet the challenges at the national level competitive examinations like CSIR NET in Mathematical Science, SET, Indian Statistical Service (ISS), etc.

Programme Outcome/Programme Learning Goals/Programme Learning Outcome:

PO1: To impart the importance of the role of approximation and mathematical approaches to analyze the real problems.

PO2: To strengthen analytical and problem-solving skill through real-time applications.

PO3: To gain practical experience in computational techniques and programming tools used in the statistical arena.

PO4: To provide a strong foundation in the best practices of collating and disseminating information.

PO5: To imbibe quality research and develop solutions to social issues.

PO6: To prepare the students to use their skills in interdisciplinary areas such as finance, health, agriculture, government, business, industry etc.

Assesment Pattern

CIA - 50%

ESE - 50%

Examination And Assesments

Evaluation pattern for full CIA courses offered:

 

The “Theory and Practical” Type of courses offered in all UG/PG programmes will be considered as Full CIA courses.

 

For this type of courses, there is no exclusive Mid Semester Examination and End Semester Examination; instead there shall be a continuous evaluation during the semester as,

 

CAC – Continuous Assessment Component

Assessment components such as Hard copy / Soft copy Assignment, Quiz, Presentation, Video Making, MOOC, Project, Demonstration, Service Learning, etc

CAT – Continuous Assessment Test

A written / Lab test would be conducted on any working day

 

The total marks for the full CIA courses would vary based on the number of hours allocated in a week for the respective course. Out of the maximum marks allotted to the respective course, 50% marks will be considered as CIA and remaining 50% as ESE based on the combinations of the evaluation components (CAC and CAT). 

MST131 - PROBABILITY THEORY (2023 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:4

Course Objectives/Course Description

 

Probability measures uncertainty and forms the foundation of statistical methods. This course makes students use measure-theoretic and analytical techniques for understanding probability concepts.

Course Outcome

CO1: Relate measure and probability concepts.

CO2: Analyze probability concepts using the measure-theoretic approach.

CO3: Evaluate conditional distributions and conditional expectations.

CO4: Make use of limit theorems in the convergence of random variables

Unit-1
Teaching Hours:12
Probability and Random variable
 

Sets – functions - Sigma field – Measurable space – Sample space – Measure – Probability as a measure - Inverse function - Measurable functions – Random variable - Induced probability space - Distribution function of a random variable: definition and properties.

Unit-2
Teaching Hours:12
Expectation and Generating functions
 

Expectation and moments: Definition and properties – Probability generating function - Moment generating functions – quantile of order p - Moment inequalities: Markov’s, Chebychev’s, Holder, Jenson and basic inequalities - Characteristic function and properties (idea and statement only).

Unit-3
Teaching Hours:12
Random Vectors
 

Random vectors – joint distribution function – joint moments - Conditional probabilities - Bayes’ theorem – conditional distributions – independence - Conditional expectation and its properties

Unit-4
Teaching Hours:12
Convergence
 

Modes of convergence: Convergence in probability, in distribution, in rth mean, almost sure convergence and their inter-relationships - Convergence theorem for expectation

Unit-5
Teaching Hours:12
Limit theorems
 

Law of large numbers - Covergence of series of independent random variables - Weak law of large numbers (Kninchine’s and Kolmogorov’s) - Kolmogorov’s strong law of large numbers - Central limit theorems for i.i.d random variables: Lindberg-Levy and Liaponov’s CLT.

Text Books And Reference Books:
  1. Rohatgi, V.K. and Salah, A.K.E, (2015), An Introduction to Probability and Statistics, 3rd Ed., John Wiley & Sons.
  2. Bhat, B.R, (2014), Modern Probability Theory, 4th Ed., New Age International.
Essential Reading / Recommended Reading
  1. Feller W, (2008), An Introduction to Probability Theory and its Applications, Volume I , 3rd Ed., Wiley Eastern.
  2. Feller W, (2008), An Introduction to Probability Theory and its Applications, Volume II,3rd Ed., Wiley Eastern.
  3. Billingsley, P. (2008). Probability and measure. John Wiley & Sons.
  4. Basu A.K, (2012), Measure Theory and Probability, 2nd Ed., PHI.
  5. Durrett R, (2010), Probability: Theory and Examples. 4th ed. Cambridge University Press, 2010.
Evaluation Pattern
  • CIA: 50%
  • ESE: 50%

MST132 - DISTRIBUTION THEORY (2023 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:4

Course Objectives/Course Description

 

Probability distributions are used in many real-life phenomena. This course makes students understand different probability distributions and model real-life problems using them.

Course Outcome

CO1: Classify different families of probability distributions.

CO2: Analyse well-known probability distributions as a special case of different families of distribution

CO3: Identify different distributions arising from sampling from the normal distribution.

CO4: Apply probability distribution in various statistical problems.

Unit-1
Teaching Hours:12
Discrete Distributions
 

Modified power series family and properties - Binomial - Geometric- Negative binomial, Logarithmic series - hypergeometric distribution and its properties.

Unit-2
Teaching Hours:12
Continuous Distributions
 

Pearsonian system of distributions - Beta, Gamma, Pareto and Normal as special cases of the Pearson family and their properties

Unit-3
Teaching Hours:12
Sampling distributions
 

Sampling distributions of the mean and variance from normal population - independence of mean and variance - chi-square, students t and F distribution and their non-central forms - Order statistics and their distributions.

Unit-4
Teaching Hours:12
Multivariate distributions
 

Bivariate Poisson, Multinomial distribution - Multivariate normal (definition only) - bivariate exponential distribution of Gumbel - Marshall and Olkin distribution - Dirichlet distribution.

Unit-5
Teaching Hours:12
Distribution of Quadratic forms
 

Quadratic forms in normal variables: distribution and roperties - Cochran’ theorem: applications.

Text Books And Reference Books:
  1. Rohatgi, V.K. and Salah, A.K.E. (2015) An Introduction to Probability and Statistics, 3rd Ed., John Wiley & Sons.
  2. Krishnamoorthy, K. (2016). Handbook of statistical distributions with applications. CRC Press
Essential Reading / Recommended Reading
  1. Feller W, (2008), An Introduction to Probability Theory and its Applications, Volume I , 3rd Ed., Wiley Eastern.
  2. Feller W, (2008), An Introduction to Probability Theory and its Applications, Volume II,3rd Ed., Wiley Eastern.
  3. Billingsley, P. (2008). Probability and measure. John Wiley & Sons.
  4. Basu A.K, (2012), Measure Theory and Probability, 2nd Ed., PHI.
  5. Durrett R, (2010), Probability: Theory and Examples. 4th ed. Cambridge University Press, 2010.
Evaluation Pattern
  • CIA: 50%
  • ESE: 50%

MST133 - MATRIX THEORY AND LINEAR MODELS (2023 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course is offered to make students understand the critical aspects of matrix theory and linear models used in different areas of statistics such as regression analysis, multivariate analysis, design of experiments and stochastic processes.

Course Outcome

CO1: Demonstrate the concepts of vector space and different operations on it.

CO2: Analyze the system of linear equations using the matrix theoretic approach.

CO3: Identify applications of matrix theory in statistical problems.

CO4: Apply matrix theory in linear models

Unit-1
Teaching Hours:12
System of linear equations
 

Matrix operations - Linear equations - row reduced and echelon form - Homogenous system of equations - Linear dependence

Unit-2
Teaching Hours:12
Vector Space
 

Vectors - Operations on vector space - subspace – null space and column space - Linearly independent sets - spanning set - bases - dimension - rank - change of basis.

Unit-3
Teaching Hours:12
Linear transformations
 

Algebra of linear transformations - Matrix representations - rank nullity theorem - determinants - eigenvalues and eigenvectors - Cayley-Hamilton theorem - Jordan canonical forms - orthogonalisation process - orthonormal basis.

Unit-4
Teaching Hours:12
Quadratic forms and special matrices useful in statistics
 

Reduction and classification of quadratic forms - Special matrices: symmetric matrices - positive definite matrices - idempotent and projection matrices - stochastic matrices - Gramian matrices - dispersion matrices

Unit-5
Teaching Hours:12
Linear models
 

Fitting the model - ordinary least squares - estimability of parametric functions - Gauss-Markov theorem - applications: regression model - analysis of variance.

Text Books And Reference Books:
  1. David C. Lay, Steven R. Lay, Judi J. McDonald (2016) Linear algebra and its applications. Pearson.
  2. Lipschutz, S., & Lipson, M. L. (2018). Schaum's Outline of Linear Algebra. McGraw-Hill Education.
Essential Reading / Recommended Reading
  1. Searle, S. R., & Khuri, A. I. (2017). Matrix algebra useful for statistics. John Wiley & Sons.
  2. Rencher, A. C., & Schaalje, G. B. (2008). Linear models in statistics. John Wiley & Sons.
  3. Khuri, A. I. (2003). Advanced calculus with applications in statistics. Hoboken, NJ: Wiley-Interscience.
  4. Gentle, J. E. (2017) Matrix algebra- Theory, Computations and Applications in Statistics. Springer texts in statistics, Springer, New York.
  5. Strang, G. (2006) Linear Algebra and its Applications: Thomson Brooks. Cole, Belmont, CA, USA.
Evaluation Pattern
  • CIA: 50%
  • ESE: 50%

MST171 - DESIGN AND ANALYSIS OF SAMPLE SURVEYS USING R (2023 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course aims to impart the concepts of survey sampling theory and the analysis of complex surveys, including methods of sample selection, estimation, sampling variance, and standard error of estimation in a finite population, development of sampling theory for use in sample survey problems and sources of errors in surveys.

Course Outcome

CO1: Understand R and R studio.

CO2: Analyze different sample survey designs and find estimators.

CO3: Identify the use of different sample survey designs.

CO4: Apply a suitable sample survey design to real-life problems.

Unit-1
Teaching Hours:15
R and R studio
 

 Getting started with R - installing R and R studio - getting help - installing and loading packages - simple arithmetic calculations - data structure – expressions - conditional statements– functions – loops - R–markdown Practical Assignments: 1. R program to illustrate different data structures 2. Defining functions and making the report in markdown

Unit-2
Teaching Hours:15
Random Sampling designs
 

 

Population - sample - sampling vs census - simple random 

sampling (SRS): with and without replacement (SRSWOR) of 

units - estimators of mean, total and variance - determination 

of sample size - sampling for proportions - Stratified sampling 

scheme: estimation and allocation of sample size -

comparison with simple random sampling schemes.

Practical Assignments:

3. Illustration of simple random sampling schemes

4. Illustration of stratified random sampling schemes

Unit-3
Teaching Hours:15
Ratio and regression estimators
 

 Unbiased ratio type estimator - ratio estimator in stratified random sampling - Difference estimator and Regression estimator - comparison of regression estimator with mean per unit and ratio estimator - regression estimator in stratified random sampling. Practical Assignments: 5. Estimation using ratio estimator 6. Estimation using regression estimator 7. Ratio estimator and regression estimator in stratified sampling

Unit-4
Teaching Hours:15
Varying probability sampling designs
 

Varying probability sampling designs With and without replacement sampling schemes: PPS and PPSWR schemes - Selection of samples - estimators: ordered and unordered estimators - Πps sampling schemes. Practical Assignments: 8. Exercise on the PPS scheme 9. Exercise on the PPSWR scheme 10. Exercise on Πps sampling scheme 

Unit-5
Teaching Hours:15
Advanced sampling designs
 

Systematic sampling scheme: estimation of population mean and variance - comparison of systematic sampling with SRS and stratified random sampling - circular systematic sampling - Cluster sampling: estimation of population mean, estimation of efficiency by a cluster sample - variance function - CO2, CO3, CO4 Department of Statistics and Data Science CHRIST (Deemed to be University) 21 determination of optimum cluster size - Sampling and nonsampling errors Practical Assignments: 11. Exercise on the systematic sampling scheme 12. Exercise on cluster sampling

Text Books And Reference Books:

1. Arnab, R. (2017). Survey sampling: Theory and Applications. Academic Press.

2. Singh, D. and Chaudharay, F.S. (2018) Theory and Analysis of Sample Survey Designs, New Age International.

3. de Micheaux, P. L., Drouilhet, R., & Liquet, B. (2013). The R software. Springer. New York.

Essential Reading / Recommended Reading

1. Cochran, W.G. (2007) Sampling Techniques, Third edition, John Wiley & Sons.

2. Singh, S. (2003). Advanced Sampling: Theory and Practice. Kluwer.

3. Des Raj and Chandhok, P. (2013) Sampling Theory, McGraw Hill.

4. Mukhopadhay, P (2009) Theory and methods of survey sampling, Second edition, PHI Learning Pvt Ltd., New Delhi.

5. Sampath, S. (2005) Sampling theory and methods, Alpha Science International Ltd., India.

6. Lumley, T. (2011). Complex surveys: a guide to analysis using R. John Wiley & Sons

Evaluation Pattern

CIA 50%

ESE 50%

MST172 - PYTHON PROGRAMMING FOR STATISTICS (2023 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course equips students with programming skill in Python and associated statistical libraries and to apply in data analysis.

Course Outcome

CO1: Demonstrate the understanding of the fundamentals of Python programming.

CO2: Implement functions and data modelling.

CO3: Analyze statistical datasets and visualize the results.

CO4: Build statistical models using various statistical libraries in python.

Unit-1
Teaching Hours:15
Introduction
 

 Installing Python - basic syntax - interactive shell - editing, saving and running a script. The concept of data types - variables - assignments - mutable type - immutable types - arithmetic operators and expressions - comments in the program - understanding error messages - Control statements - operators.

Practical Assignments:

1. Lab exercise on data types

2. Lab exercise on arithmetic operators and expressions

3. Lab exercise on Control statements.

Unit-2
Teaching Hours:15
Design with functions
 

Introduction to functions - inbuilt and user defined functions - functions with arguments and return values - formal vs actual arguments - named arguments - Recursive functions - Lambda function - OOP Concepts - classes - objects - attributes and methods - defining classes - inheritance - polymorphism.

Practical Assignments:

4. Lab exercise on inbuilt and user-defined functions

5. Lab exercise on Recursive and Lambda function

6. Lab exercise on OOP Concepts

Unit-3
Teaching Hours:15
Statistical Analysis -I using Pandas
 

Introduction to Pandas - Pandas data series - Pandas data frames - data handling - grouping - Descriptive statistical analysis and Graphical representation

Practical Assignments:

7. Lab exercise on Pandas data series, frame, handling and grouping

8. Lab exercise on statistical analysis 

Unit-4
Teaching Hours:15
Statistical Analysis - II using Pandas
 

 Hypothesis testing - data modeling - linear regression models - logistic regression model.

Practical Assignments:

9. Lab exercise on Hypothesis testing

10. Lab exercise on regression modellin

Unit-5
Teaching Hours:15
Visualization Using Seaborn and Matplotlib
 

Line graph - Bar chart - Pie chart - Heat map - Histogram - Density plot - Cumulative frequencies - Error bars - Scatter plot - 3D plot.

Practical Assignments:

11. Lab exercise on graphical and diagrammatic representation.

12. Lab exercise on the density plot

13. Lab exercise on scatter and 3D plo

Text Books And Reference Books:

1.Lambert, K. A. (2018). Fundamentals of Python: first programs. Cengage Learning. 0. Haslwanter, T. (2016).

2.An Introduction to Statistics with Python. Springer International Publishing.

Essential Reading / Recommended Reading

1. Unpingco, J. (2016). Python for probability, statistics, and machine learning, Vol.1, Springer International Publishing.

2. Anthony, F. (2015). Mastering pandas. Packt Publishing Ltd. 

Evaluation Pattern

CIA 50%

ESE 50%

MST231 - RESEARCH METHODOLOGY AND LATEX (2023 Batch)

Total Teaching Hours for Semester:30
No of Lecture Hours/Week:3
Max Marks:50
Credits:2

Course Objectives/Course Description

 

To acquaint students with different methodologies in statistical research and to make them prepare scientific articles using LaTeX.

Course Outcome

CO1: Define a research problem.

CO2: Identify a suitable methodology for solving the research problem

CO3: Create scientific articles using LaTeX.

Unit-1
Teaching Hours:15
Fundamentals of research
 

Objectives - Motivation - Utility - Concept of theory - empiricism - deductive and inductive theory - Characteristics of scientific method - Understanding the language of research- Concept - Construct - Definition - Variable - Research Process Problem Identification & Formulation - Research Question – Investigation Question - Logic & Importance

Unit-2
Teaching Hours:15
Scientific writing
 

Principles of mathematical writing - LaTeX: installing packages and editor, preparing title page - mathematical expressions - tables - importing graphics - bibliography - writing a research paper - survey article - thesis writing - Beamer: preparing presentations

Text Books And Reference Books:

1. Kothari, C. R. and Garg, G. (2014). Research methodology: Methods and techniques. 3rd Ed., New Age International.

2. L. Lamport (2014), LaTeX, a Document Preparation System, 2nd ed, Addison-Wesley.

Essential Reading / Recommended Reading

1. Grätzer, G. (2013). Math into LATEX. Springer Science & Business Media.

Evaluation Pattern

CIA - 50%

ESE - 50%

MST232 - STATISTICAL INFERENCE I (2023 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course is designed to provide the strong conceptual foundations of testing of hypotheses, procedures for testing hypotheses, likelihood ratio tests, sequential tests and non-parametric tests.

Course Outcome

CO1: Apply the procedures of testing hypotheses for solving real-life problems.

CO2: Develop appropriate tests for testing specific statistical hypotheses.

CO3: Draw conclusions about the population with the help of various estimation and testing procedures.

CO4: Apply various non-parametric tests and draw conclusions to real-life problems.

Unit-1
Teaching Hours:12
Generalized Neyman-Pearson Lemma and One-sided tests
 

Monotone Likelihood Ratio (MLR) property - Testing in one-parameter exponential families - Generalised Neyman-Pearson lemma (Statement only) - Unbiased and invariant tests - Locally most powerful tests

Unit-2
Teaching Hours:12
Uniformly most powerful tests
 

One-sided uniformly most powerful tests - Unbiased and Uniformly Most Powerful Unbiased tests for different two-sided hypothesis - Extension of these results to Pitman family when only upper or lower end depends on the parameters - UMP test from α-similar tests and α-similar tests with Neyman structure.

Unit-3
Teaching Hours:12
Likelihood Ratio Test (LRT) procedures
 

Likelihood ratio test (LRT) - asymptotic properties - LRT for the parameters of binomial and normal distributions - Generalized likelihood ratio tests - Chi-

Square tests - t-tests - F-tests

Unit-4
Teaching Hours:12
Basics of non-parametric tests
 

Non-parametric tests: Sign test - Chi-square tests - Kolmogorov-Smirnov one sample and two samples tests - Median test - Wilcoxon Signed Rank test - Mann- Whitney U-test - Test for Randomness - Runs up and runs down test - Wald–Wolfowitz run test for equality of distributions - Kruskal–Wallis one-way analysis of variance - Friedman’s two-way analysis of variance - Power and asymptotic relative efficiency.

Unit-5
Teaching Hours:12
Confidence intervals
 

Large sample confidence interval - shortest length confidence interval - Methods of finding confidence interval: Inversion of the test statistic, pivotal quantities,

pivoting CDF- evaluation of confidence interval: size and coverage probability.

Text Books And Reference Books:

1. Rohatgi, V. K. and Saleh, A.K.M. (2015). An Introduction to Probability and Statistics, John Wiley and Sons.

Essential Reading / Recommended Reading

1. Srivastava, M.K., Khan, A.H. and Srivastava, N. (2014). Statistical Inference- Testing of Hypothesis, Prentice Hall India, New Delhi.

2. Rajagopalan, M. and Dhanavanthan, P. (2012). Statistical Inference, PHI Learning Pvt Ltd, New Delhi.

3. Kendall, M.G. and Stuart, A. (1967). The Advanced Theory of Statistics, vol 2, 2nd edition. Mc-Millan, New York.

4. Kale, B. K. and Muralidharan, K. (2015). Parametric Inference: An Introduction. Alpha Science Int. Ltd.

5. Mukhopadhyay, P.(2015): Mathematical Statistics, Books and Allied (P) Ltd., Kolkata.

6. Gibbons J.K. (1971). Non-Parametric Statistical Inference, McGraw Hill.

7. Lehmann, E. L. and Romano, J. P. (2005). Testing Statistical Hypotheses, 2/e, JohnWiley, NewYork.

Evaluation Pattern

CIA - 50%

ESE - 50%

MST233 - STOCHASTIC PROCESSES (2023 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:4

Course Objectives/Course Description

 

To equip the students with theoretical and practical knowledge of stochastic models which are used in economics, life sciences, engineering etc.

Course Outcome

CO1: Apply the Markov models to solve the real world problems.

CO2: Identify the nature of Markov chains model to apply it to real world statistical data.

CO3: Identify the nature of Markov chains model to apply it to real world statistical data.

Unit-1
Teaching Hours:12
Introduction
 

A sequence of random variables - definition and classification of the stochastic process - autoregressive processes and Strict Sense and Wide Sense stationary processes.

Unit-2
Teaching Hours:12
Discrete time Markov chains
 

Markov Chains: Definition, Examples - Transition probability matrix -  Chapman-Kolmogorv equation - classification of states - limiting and stationary distributions - ergodicity - discrete renewal equation and basic limit theorem - Absorption probabilities - Criteria for recurrence - Generic application: hidden Markov models.

Unit-3
Teaching Hours:12
Continuous time Markov chains and Poisson process
 

Transition probability function - Kolmogorov differential equations - Poisson process: homogenous process, inter-arrival time distribution, compound process - Birth and death process - Service applications: Queuing models- Markovian models.

Unit-4
Teaching Hours:12
Branching process
 

Galton-Watson branching processes - Generating function - Extinction probabilities - Continuous-time branching processes - Extinction probabilities - Branching processes with general variable lifetime.

Unit-5
Teaching Hours:12
Renewal process and Brownian motion
 

Renewal equation - Renewal theorem - Generalisations and variations of renewal processes -  Brownian motion - Introduction to Markov renewal processes.

Text Books And Reference Books:

1.Karlin, S. and Taylor, H.M. (2014). A first course in stochastic processes. Academic Press.

2.S. M. Ross (2014). Introduction to Probability Models. Elsevier.

 

Essential Reading / Recommended Reading

1.Feller, W. (2008) An Introduction to Probability Theory and its Applications, Volume I&II , 3rd Ed., Wiley Eastern.

2. J. Medhi (2009) Stochastic Processes, 3rd Edition, New Age International.

3. Dobrow, R.P. (2016), Introduction to Stochastic Processes with R, Wiley Eastern.

4. Cinlar, E. (2013). Introduction to stochastic processes. Courier Corporation.

Evaluation Pattern

CIA 50%

ESE 50%

 

MST271 - APPLIED REGRESSION ANALYSIS (2023 Batch)

Total Teaching Hours for Semester:90
No of Lecture Hours/Week:8
Max Marks:150
Credits:5

Course Objectives/Course Description

 

Regression models are mainly used to establish a relationship among variables and predict future values. It got applications in various domains such as finance, life science, management, psychology, etc. This course is designed to impart knowledge of statistical model building using regression techniques. 

Course Outcome

CO1: Formulate simple and multiple regression models.

CO2: Identify the correct regression model for the given problem.

CO3: Apply non-linear regression in real-life problems.

CO4: Analyse the robustness of the regression model.

Unit-1
Teaching Hours:18
Linear regression model Linear Regression Model
 

 Simple and multiple - Least squares estimation - Properties of the estimators - Maximum likelihood estimation - Estimation with linear restrictions - Hypothesis testing - confidence intervals.

Practical Assignments:

1. Build a simple linear model and interpret the data.

2. Construct a confidence interval for the simple linear model

3. Build a multiple linear model and estimate its parameters.

4. Construct a confidence interval for multiple linear

Unit-2
Teaching Hours:18
Model adequacy
 

 Residual analysis - Departures from underlying assumptions - Effect of outliers - Collinearity - Nonconstant variance and serial correlation - Departures from normality - Diagnostics and remedies. Practical Assignments: 5. Carry out residual analysis and validate the model assumptions. 6. Construct residual plots for checking outliers, leverage, and influential points. 7. Checking the assumption of homoscedasticity and its remedial measures 8. Detecting multicollinearity and its remedial measures.

Unit-3
Teaching Hours:18
Model Selection
 

 Selection of input variables and model selection - Methods of obtaining the best fit - stepwise regression - Forward selection and backward elimination

Practical Assignments:

9. Selecting the best model using step-wise regression.

10. Selecting the best model using Forward and backward 

Unit-4
Teaching Hours:18
Nonlinear regression
 

Nonlinear regression Introduction to general non-linear regression - least-squares in non-linear case - estimating the parameters of a non-linear system - re-parameterization of the model - logistic regression- Non-linear growth models

Practical Assignments:

11. Estimate parameters in non-linear models using the least square procedure

Unit-5
Teaching Hours:18
Robust regression
 

 Linear absolute deviation regression - M estimators: properties - Breakdown and Efficiency points - Bootstrapping in Regression- Jackknife techniques and least squares approach based on M-estimators.

Practical Assignments:

12. Illustrate resampling procedures in regression models.

13. Build a regression model robust regression procedure.

Text Books And Reference Books:

1. Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to linear regression analysis. John Wiley & Sons.

 

Essential Reading / Recommended Reading

Recommended references:

1. S.N Sivanandam, S.N Deepa (2018). Principles of soft computing. Wiley India.
2. S Lovelyn Rose, L Ashok Kumar, Karthika Renuka (2019). Deep Learning using Python. Wiley India.

3. Francois Chollet (2017). Deep Learning with Python. Manning Publishing.

4. Andreas C. Muller & Sarah Guido (2017). Introduction to Machine Learning with Python. O’Reilly Media, Inc.

5. Chatterjee, S., & Hadi, A. S. (2015). Regression analysis by example. John Wiley & Sons.

6. Draper, N. R., & Smith, H. (2014). Applied regression analysis. 3rd edition. John Wiley & Sons. 

Evaluation Pattern

CIA 50%

ESE 50%

MST273A - PRINCIPLES OF DATA SCIENCE AND DATABASE TECHNIQUES (2023 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course provides a strong foundation for data science and application area related to it and caters for the underlying core concepts and emerging technologies in data science.

Course Outcome

CO1: Understand the fundamental concepts of data science.

CO2: Understand various machine learning algorithms used in data science process.

CO3: Design effective queries for relational schema.

CO4: Analyze the various types of Data Warehouse models.

Unit-1
Teaching Hours:15
Introduction to Data Science
 

Definition – Big Data and Data Science Hype – Why data science – Getting Past the Hype – The Current Landscape – Who is a Data Scientist? - Data Science Process Overview – Defining goals – Retrieving data – Data preparation – Data exploration – Data modeling – Presentation. Data science ethics – valuing different aspects of privacy – The five C’s of data.

Unit-2
Teaching Hours:15
Machine Learning
 

 

MACHINE LEARNING Machine learning – Modeling Process – Training model – Validating model – Predicting new observations –Supervised learning algorithms – Unsupervised learning algorithms

Practical Assignments:

1. Implement any one supervised algorithm

2. Implement any one unsupervised algorithm

Unit-3
Teaching Hours:15
Introduction to Relational Database
 

INTRODUCTION TO RELATIONAL DATABASE Overview of DBMS, Data Models, Database Languages, Database Administrator, Database Users, Three Schema architecture of DBMS. Basic concepts, Design Issues, Mapping Constraints, Keys, Entity-Relationship Diagram, Weak Entity Sets, Extended E-R features

Practical Assignments: 1. ER diagram

Practical Assignments:

4. Lab Exercise on Database Design

5. Top-Down Approach

6. Bottom-up Approach 

Unit-4
Teaching Hours:15
QUERY AND NORMALIZATION
 

SQL and Integrity Constraints, Concept of DDL, DML, DCL. Basic Structure, Set operations, Aggregate Functions, Null Values, Domain Constraints, Referential Integrity Constraints, assertions, views, Nested Subqueries, stored procedures – functions- cursors Functional Dependency, Different anomalies in designing a Database, Normalization: using functional dependencies, Boyce-Codd Normal Form

Practical Assignments:

7. Simple Query

8. Sub Query

9. Procedures

10. Cursors

Unit-5
Teaching Hours:15
Introduction to Data Warehouse
 

INTRODUCTION TO DATA WAREHOUSE Defining Features, Database and Data Warehouses, Architectural Types, Overview of the Components, Metadata in the Data warehouse, The Star Schema, Star Schema Keys, Advantages of the Star Schema, Star Schema: Examples, Snowflake Schema, Aggregate Fact Tables, ETL process, Reporting services.

Practical Assignments:

11. Analysis Services

12. ETL process

13. Reporting Service

Text Books And Reference Books:

 

1. Davy Cielen, Arno D. B. Meysman, Mohamed Ali (2016), Introducing Data Science, Manning Publications Co.

2. Thomas Cannolly and Carolyn Begg, (2007), Database Systems, A Practical Approach to Design, Implementation and Management”, 3rd Edition, Pearson Education. 

Essential Reading / Recommended Reading

[1] Data Science from Scratch: First Principles with Python, Joel Grus, O’Reilly, 1st edition, 2015

[2] Mining of Massive Datasets, Jure Leskovec, Anand Rajaraman, Jeffrey David Ullman, Cambridge University Press, 2nd edition, 2014

[3] Sinan Ozdemir, Principles of Data Science learn the techniques and math you need to start making sense of your data. Birmingham Packt December, 2016. [4]D J Patil, Hilary Mason, Mike Loukides, Ethics and Data Science, O’ Reilly, 2018. 

Evaluation Pattern

CIA 50%+ESE 50%

MST273B - BIOSTATISTICS (2023 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course provides an understanding of various statistical methods in describing and analyzing biological data. Students will be equipped with an idea about the applications of statistical hypothesis testing, related concepts and interpretation of biological data.

Course Outcome

CO1: Demonstrate the understanding of basic concepts of biostatistics and the process involved in the scientific method of research.

CO2: Identify how the data can be appropriately organized and displayed.

CO3: Analyze the data based on various discrete and continuous probability distributions

CO4: Apply parametric and non-parametric methods of statistical data analysis.

CO5: Demonstrate the concepts of Epidemiology

Unit-1
Teaching Hours:20
Introduction to Biostatistics
 

Presentation of data - graphical and numerical representations of data - Types of variables, measures of location - dispersion and correlation - inferential statistics - probability and distributions - Binomial, Poisson, Negative Binomial, Hyper geometric and normal distribution. Sensitivity, Specificity, Positive predictive value, Negative predictive value. ROC Curves.

Practical Assignments:

1. Exercise on the representation of data

2. Exercise on reporting data by descriptive statistics

Unit-2
Teaching Hours:20
Parametric and Non - Parametric methods
 

Parametric methods - one sample t-test - independent sample t-test - paired sample t-test - one-way analysis of variance - two-way analysis of variance - analysis of covariance - repeated measures of analysis of variance - Pearson correlation coefficient - Non-parametric methods: Chi-square test of independence and goodness of fit - Mann Whitney U test - Wilcoxon signed-rank test - Kruskal Wallis test - Friedman’s test - Spearman’s correlation test.

Practical Assignments:

1. Exercise on various parametric methods of analysis

2. Exercise on various non-parametric methods of analysis

Unit-3
Teaching Hours:20
Generalized linear models
 

Review of simple and multiple linear regression - introduction to generalized linear models - parameter estimation of generalized linear models - models with different link functions - binary (logistic) regression - estimation and model fitting - Poisson regression for count data - mixed effect models and hierarchical models with practical examples.

Practical Assignments:

1. Exercise on simple linear and multiple linear regression

2. Exercise on logistic regression

3. Exercise on Poisson regression

Unit-4
Teaching Hours:15
Epidemiology
 

 

Introduction to epidemiology, measures of epidemiology, observational study designs: case report, case series correlational studies, cross-sectional studies, retrospective and prospective studies, analytical epidemiological studies-case control study and cohort study, odds ratio, relative risk, the bias in epidemiological studies.

Practical Assignments:

1. Exercise on analysis of observational study data

2. Exercise on analysis of cross-sectional study data

3. Exercise on analysis of case-control study data

4. Exercise on analysis of cohort study data

Text Books And Reference Books:

1. Rosner, B. (2015). Fundamentals of biostatistics. Cengage learning.

2. Dobson, A. J., & Barnett, A. G. (2018). An introduction to generalized linear models. CRC press.

3. Gordis, L. (2013). Epidemiology e-book. Elsevier Health Sciences.

Essential Reading / Recommended Reading

1. Marcello Pagano and Kimberlee Gauvreau (2018), Principles of Biostatistics, 2nd Edition, Chapman and Hall/CRC press

2. David Moore S. and George McCabe P., (2017) Introduction to practice of statistics, 9th Edition, W. H. Freeman.

3. Sundar Rao and Richard J., (2012) Introduction to Biostatistics and research methods, PHI Learning Private limited, New Delhi.

4. Abhaya Indrayan and Rajeev Kumar M., (2018) Medical Biostatistics, 4th Edition,Chapman and Hall/CRC Press.

5. Gordis Leon (2018), Epidemiology, 6th Edition, Elsevier, Philadelphia

6. Park K., (2019), Park's Text Book of Preventive and Social Medicine, Banarsidas Bhanot, Jabalpur.

Evaluation Pattern

CIA-50%

ESE -50%

MST273C - OPTIMIZATION TECHNIQUES (2023 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course is designed to train the students to develop their modelling skills in mathematics through various methods of optimization. The course helps the students to understand the theory of optimization methods and algorithms developed for solving various types of optimization problems.

Course Outcome

CO1: Understand and apply linear programming problems

CO2: Apply one-dimensional and multidimensional optimization problems.

CO3: Understand multidimensional constrained and unconstrained optimization problems.

CO4: Apply geometric and dynamic programming problems.

CO5: Solve nonlinear problems through its linear approximation.

Unit-1
Teaching Hours:15
Linear Programming Problems (LPP)
 

Introduction to optimization – convex set and convex functions –simplex method: iterative nature of simplex method – additional simplex method: duality concept - dual simplex method - generalized simplex algorithm - revised simplex method: revised simplex algorithm – development of the optimality and feasibility Conditions.

 

Practical Assignments:

1. Formulate the LPP.

2. Solve the LPP using simplex method.

3. Solve the LPP using revised simplex method.

Unit-2
Teaching Hours:15
Integer Linear Programming
 

Branch and bound algorithm – cutting plane algorithm – transportation problem: north-west method, least-cost method, vogel’s approximation and method of multipliers – assignment problem: mathematical statement, Hungarian method, variation of assignment problems.

Practical Assignments:

4. Solve integer LPP by cutting plane method.

5. Formulate and solve transportation problems.

6. Formulate and solve assignment problems.

Unit-3
Teaching Hours:15
Non-linear Programming
 

Introduction – unimodal function – one-dimensional optimization: Fibonacci method – golden Section Method – quadratic interpolation methods - cubic interpolation methods – direct root method: newton method and quasi newton method – Multidimensional unconstrained optimization: univariate method– Hooks and Jeeves method – Fletcher – Reeves method - Newton’s method and quasi newton’s method.

Practical Assignments:

7. Solve a non LPP problem.

8. Solve an unconstrained optimization problem by a univariate method

Unit-4
Teaching Hours:15
Classical optimization techniques
 

Single variable optimization – multivariable optimization with no constraints: semi-definite case and saddle point – multivariable optimization with equality constraints: direct substitution –method of constrained variation – method of Lagrange multipliers - Kuhn-Tucker conditions - constraint qualification – convex programming problem.

Practical Assignments:

9. Solve a single variable optimization problem.

10. Solve multivariable optimization problems with equality constraints.

11. Solve a convex optimization problem.

Unit-5
Teaching Hours:15
Geometric and Dynamic programming
 

Unconstrained minimization problem – solution of an unconstrained geometric programming problem using arithmetic- geometric inequality method – primal dual relationship -constrained minimization - dynamic programming: Dynamic programming algorithm – solution of linear programming problem by dynamic programming.

Practical Assignments:

12. Formulate and solve a dynamic programming problem.

13. Solve LPP through dynamic programming problems.

14. Solve a geometric programming problem.

Text Books And Reference Books:

1. H. A. Taha (2017), Operations Research – An Introduction, 10th Edition, Prentice – Hall of India, New Delhi.

2. S. S. Rao (2019), Engineering Optimization, 5th Edition, New Age International Pvt. Ltd., Publishers, Delhi.

Essential Reading / Recommended Reading

1. J.K. Sharma (2010), Quantitative Techniques for Managerial Decisions, Macmillan.

2. Hadley, G. (2002), Linear Programming, Addison Wesley.

3. G. Srinivasan (2007), Operations Research: Principles & Applications, Prentice Hall of India, New Delhi, India.

Evaluation Pattern

CIA-50%

ESE-50%

MST331 - STATISTICAL INFERENCE II (2023 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course is designed to provide the strong conceptual foundations of testing of hypothesis, procedures of testing hypothesis, likelihood ratio tests, sequential tests and non-parametric tests

Course Outcome

CO1: Apply the procedures of testing hypotheses for solving real-life problems.

CO2: Develop appropriate tests for testing specific statistical hypotheses.

CO3: Draw conclusions about the population with the help of various estimation and testing procedures.

CO4: Apply various non-parametric tests and draw conclusions to real-life problems.

Unit-1
Teaching Hours:12
Generalized Neyman-Pearson Lemma and One-sided tests
 

Monotone Likelihood Ratio (MLR) property - Testing in one-parameter exponential families - Generalised Neyman-Pearson lemma (Statement only) - Unbiased and invariant tests - Locally most powerful tests

Unit-2
Teaching Hours:12
Uniformly most powerful tests
 

One-sided uniformly most powerful tests - Unbiased and Uniformly Most Powerful Unbiased tests for differenttwo-sided hypothesis - Extension of these results to Pitman family when only upper or lower end depends onthe parameters - UMP test from α-similar tests and α-similar tests with Neyman structure.

Unit-3
Teaching Hours:12
Likelihood Ratio Test (LRT) procedures
 

Likelihood ratio test (LRT) - asymptotic properties -LRT for the parameters of binomial and normal distributions - Generalized likelihood ratio tests - Chi-Square tests - t-tests - F-tests

Unit-4
Teaching Hours:12
Basics of non-parametric tests
 

Non-parametric tests: Sign test - Chi-square tests - Kolmogorov-Smirnov one sample and two samples tests -Median test - Wilcoxon Signed Rank test - Mann-Whitney U-test - Test for Randomness - Runs up and runs down test - Wald–Wolfowitz run test for equality of distributions - Kruskal–Wallis one-way analysis of variance - Friedman’s two-way analysis of variance -Power and asymptotic relative efficiency.

Unit-5
Teaching Hours:12
Confidence intervals
 

 Large sample confidence interval - shortest length 

confidence interval - Methods of finding confidence 

interval: Inversion of the test statistic, pivotal quantities, 

pivoting CDF- evaluation

Text Books And Reference Books:

Rohatgi, V. K. and Saleh, A.K.M. (2015). An Introduction to Probability and Statistics, John Wiley and Sons.

Essential Reading / Recommended Reading
  1. Srivastava, M.K., Khan, A.H. and Srivastava, N. (2014). Statistical Inference- Testing of Hypothesis, Prentice Hall India, New Delhi.
  2. Rajagopalan, M. and Dhanavanthan, P. (2012). Statistical Inference, PHI Learning Pvt Ltd, New Delhi.
  3. Kendall, M.G. and Stuart, A. (1967). The Advanced Theory of Statistics, vol 2,

2nd edition. Mc-Millan, New York.

 

  1. Kale, B. K. and Muralidharan, K.  (2015). Parametric Inference: An Introduction. Alpha Science Int. Ltd.
  2. Mukhopadhyay, P.(2015): Mathematical Statistics, Books and Allied (P) Ltd., Kolkata.
  3. Gibbons J.K. (1971).  Non-Parametric Statistical Inference, McGraw Hill.Lehmann, E. L. and Romano, J. P. (2005). Testing Statistical Hypotheses, 2/e, JohnWiley, NewYork.
Evaluation Pattern
CIA-50%

ESE-50%

MST371 - TIME SERIES ANALYSIS (2023 Batch)

Total Teaching Hours for Semester:90
No of Lecture Hours/Week:8
Max Marks:150
Credits:5

Course Objectives/Course Description

 

This   course   considers   statistical   techniques   to    evaluate    processes    occurringthrough   time.   It   introduces   students   to    time    series    methods    and    theapplicationsofthesemethodstodifferenttypesof   data   in   various   fields.   Timeseriesmodelling   techniques   including   AR,   MA,   ARMA,   ARIMA   and   SARIMAwillbeconsidered   with   reference   to   their   use   in   forecasting.   The   objective   ofthiscourseistoequipstudentswith   various   forecasting   techniques   and   tofamiliarize themselves

Course Outcome

CO1: Demonstrate of basic concepts of analyzing time series, including white noise, trend, seasonality, cyclical component, auto-covariance and autocorrelation function.

CO2: Apply the concept of stationarity to the analysis of time series data in various contexts.

CO3: Select the appropriate model, to fit parameter values, examine residual analysis, and to carry out the forecasting calculation.

CO4: Apply various techniques of seasonal time series models, including the seasonal autoregressive integrated moving average (SARIMA) models and Winters exponential smoothing.

CO5: Demonstrate the principles behind modern forecasting techniques, which includes obtaining the relevant data and carrying out the necessary computation using R software.

Unit-1
Teaching Hours:18
Basic concepts in time series analysis
 

Stochastic Process - Time series as a discrete parameter stochastic process Auto – Covariance - Autocorrelation and their properties - Exploratory time series analysis graphical analysis - classical decomposition model - concepts of trend, seasonality and cycle - Estimation of trend and seasonal components-Elimination of trend. Seasonality - Method of differencing - Moving average smoothing, Method of seasonal differencing

 

Practical Assignments:

1.Graphical representation of time series, plots of ACF and

PACF and their interpretation

2.Examples of trend, seasonal and cyclical time series and estimation of trend and

seasonal components

3.Exercise on Moving average smoothing to eliminate trend and illustration on the

method of differencing to eliminate trend and seasonality. 4.Exercise on least-square fitting to estimate and eliminate the trend component

 

Unit-2
Teaching Hours:18
Stationary time series models
 

Stationary time series models - Concepts of weak and strongstationarity – General linear Process - Auto-Regressive(AR),MovingAverage(MA)andAuto-RegressiveMovingAverage(ARMA)processes – theirproperties -conditionsforstationarity and invertibility -model identification based onACF and PACF- Maximum likelihood estimation – YuleWalkerEstimation-orderselection(AICandBIC)-Residual Analysis- - Box Jenkins methodology to theidentificationofstationarytime

 

seriesmodels

 

PracticalAssignments:

 

5.ExerciseonfittingARmodel

 

6.  ExerciseonfittingMAmodel

 

7.  Exerciseonfitting ARMAmodel

 

8.Model-identificationusing ACFandPACF,ModelselectionusingAIC andBIC

 

9.ResidualanalysisanddiagnosischeckforAR, MAandARMA models

Unit-3
Teaching Hours:18
Non-stationary time series models
 

 

Concept of non-stationarity - Spurious trends and regressions- unit root tests : Dickey-Fuller (DF) test - Augmented Dickey- Fuller(ADF) test – Auto-Regressive Integrated Moving

Average(ARIMA(p,d,q)) models - Difference equation form

of ARIMA- Random shock form of ARIMA - An inverted form of ARIMA

Practical Assignments:

10.Exercise on the identification of non-stationary series from various plots.

11.Exercise on testing non-stationarity using ADF test,

Exercise on fitting ARIMA models.

12.Residual analysis and diagnosis check for ARIMA model.

Unit-4
Teaching Hours:18
Seasonal time series models
 

Analysis of seasonal models - parsimonious models for seasonal time series - Seasonal unit root test (HEGY test) - General multiplicative seasonal models - Seasonal ARIMA models - estimation - Residual analysis for seasonal time series.

 Practical Assignments:

 13.  Exercise on the identification of additive and Multiplicative time series

 14.Exercise on testing the presence of seasonality and on fitting Seasonal ARIMA

  models

 15.  Residual analysis and diagnosis check for Seasonal ARIMA model

Unit-5
Teaching Hours:18
Forecasting Techniques
 

In sample and out of sample forecast - Simple exponential and

moving average smoothing - Holt Exponential Smoothing - Winter exponential smoothing - Forecasting trend and

seasonality in Box Jenkins model:- Method of minimum mean squared error (MMSE) forecast - their properties – forecast- error

 Practical Assignments:

16.Exercise on Simple exponential smoothing and Holt Exponential Smoothing

17.Exercise on Winters exponential smoothing. 18.Exercise on forecasting using ARIMA models. 19.Exercise on forecasting using seasonal ARIMA models.

 

Text Books And Reference Books:

1.  Box,G.E.,Jenkins, G.M.,Reinsel, G.C.,&Ljung,G.M.(2015).Timeseriesanalysis:forecastingandcontrol.JohnWiley&Sons.

2.  Chatfield, C., & Xing, H. (2019). The analysis of time series: an introduction with R.CRCPress.

Essential Reading / Recommended Reading

1.  Hamilton, J. D.(2020).Timeseriesanalysis.Princetonuniversitypress.

2.  Brockwell, P. J., & Davis, R. A. (2016). Introduction to time series and forecasting.springer.

Evaluation Pattern

CIA 50%

ESE 50%

MST372 - STATISTICAL MACHINE LEARNING (2023 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

Machine learning has a wide array of applications that belongs to different fields, such as biomedical research, reliability of large structures, space research, digital marketing, etc. This course will equip students with a wide variety of models and algorithms for machine learning and prepare students for research or industry application of machine learning techniques. 

Course Outcome

CO1: Demonstrate the understanding of basic concepts of statistical machine learning.

CO2: Apply classification algorithms for qualitative data.

CO3: Analyze high dimensional data using principal component regression learning algorithms.

CO4: Construct classification and regression trees by random forests.

CO5: Create a statistical learning model using support vector machines.

Unit-1
Teaching Hours:15
Statistical learning
 

Statistical learning: definition-prediction accuracy and model interpretability-supervised and unsupervised learning-assessing model accuracy- important problems in data mining: classification, regression, clustering, ranking, density estimation- Concepts: training and testing, cross-validation, overfitting, bias/variance tradeoff, regularized learning equation- simple and multiple linear regression algorithms

 Practical Assignments:

1.     Lab exercise on data preparation and using simple linear regression

2.     Lab exercise on model assessment simple linear regression

3.     Lab exercise on data preparation with multiple linear regression

Unit-2
Teaching Hours:15
Classification algorithms
 

Logistic model- training and testing the model-linear discriminant analysis-quadratic discriminant analysis- Use of Bayes’ theorem-k- nearest neighbours - Naive Bayes’- Adaboost

 Practical Assignments:

4.     Lab exercise on the logistic model

5.     Lab exercise on discriminant analysis

6.     Lab exercise on  Naïve Bayes’ and k-NN classifiers

7.     Lab exercise on  Adaboost

Unit-3
Teaching Hours:15
Linear model selection and regularization
 

Optimal model-shrinkage methods: ridge and lasso regression-Dimension reduction methods: principal component (PC) regression and partial least square (PLS) regression: Non-linear models: regression splines-polynomial – Generalized additive models

 Practical Assignments:

8.     Lab exercise on ridge regression

9.     Lab exercise on Lasso regression

10.     Lab exercise on PC regression

11.     Lab exercise on PLS regression

Unit-4
Teaching Hours:15
Tree-based methods
 

Decision tree-regression trees - bagging - random forests - boosting - classification trees-boosting-tree vs linear models

 Practical Assignments:

12.     Lab exercise on decision trees

13.     Lab exercise on regression trees

14.     Lab exercise on random forests

15.     Lab exercise on classification trees

Unit-5
Teaching Hours:15
Support vector machines and resampling procedures
 

Maximal classifier-support vector classifiers-support - rank boost (ranking algorithm) - hierarchical Bayesian modelling for density - resampling techniques-bootstrap- clustering algorithms: K-means algorithm. 

Practical Assignments:

16.     Lab exercise on SVM classifier

17.     Lab exercise on rank boost algorithm

18.     Lab exercise on kernel density estimation

19.     Lab exercise on k-means clustering

Text Books And Reference Books:
  1. James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, p. 18). New York: springer.
Essential Reading / Recommended Reading

1. Gutierrez, D. D. (2015). Machine learning and data science: an introduction to statistical learning methods with R. Technics Publications.

2. Müller, A. C., & Guido, S. (2016). Introduction to machine learning with Python: a guide for data scientists. “O’Reilly Media, Inc.".
3. Murphy, K. P. (2012). Machine learning: a probabilistic perspective. MIT press 

Evaluation Pattern

CIA 50% + ESE 50%

MST373A - JAVA PROGRAMMING FOR DATA SCIENCE (2023 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:3

Course Objectives/Course Description

 

Java programming is essential tool for data science and statistical computation. This course enables students to create programs in Java which can be used for statistical analysis

Course Outcome

CO1: Demonstrate comprehensive understanding of Java.

CO2: Implement libraries and object-oriented structures.

CO3: Design programs to handle files of different formats.

CO4: Analyze data and visualize using appropriate libraries.

Unit-1
Teaching Hours:11
Introduction
 

Introduction Installing java Development kit - Java JVM, JRE and JDK - Working with the Terminal –First Program – primitive data Types:– Variables and constants - Operators - Input and Output - Expressions & Blocks – Comment, Conditional Statements.

Practical Assignments:

1. Lab exercise on data types using various operators in Java

2. Lab exercise on control structures

Unit-2
Teaching Hours:11
Data structures in Java
 

 Primitive data structure and Non-primitive data structure - Array Processing - Multi-dimensional Arrays - String Methods - String Manipulation – Regular Expressions

Practical Assignments:

3. Lab exercise on Arrays

4. Lab exercise on Strings 

Unit-3
Teaching Hours:14
Objects Encapsulation and Classes
 

Objects - Encapsulation – Classes – Inheritance – Inheritance Hierarchies - Polymorphism – Abstraction – Protected Classes – Exceptions –Assertions –Loggin – Generic Programming- Operations in Dictionaries Practical Assignments: 5. Lab exercise on classes and objects 6. Lab exercise on exception handling and assertions 7. Lab exercise on dictionaries

8. Lab exercise on strings and regular expressions

9. Lab exercise on dictionaries

Unit-4
Teaching Hours:14
Data Science in Java
 

Data Science Libraries- data processing library, Math and Stats libraries, machine learning and data mining libraries. Standard Java Library -Collections-Input-Output,Acessing Data-CSV,JSON,DataFrames.

Practical Assignments:

8. Lab exercise on handling CSV files

9. Lab exercise on handling JSON.

Unit-5
Teaching Hours:10
Statistical Data Analysis and Data Visualization
 

Statistical Data Analysis and Data Visualization Working with mean median mode, hypothesis testing, Regression Analysis. Understanding plots and graphs

Practical Assignments:

10. Lab exercise on data visualization

Text Books And Reference Books:

Horstmann, C. S. (2019) Core Java (TM) Volume 1: Fundamentals. Pearson Education India

Essential Reading / Recommended Reading

1. Bloch, J. (2016). Effective java. Pearson Education India. Schildt, H., & Coward, D. (2014). Java: the complete reference. New York: McGraw-Hill Education-

Evaluation Pattern

CIA 50% + ESE 50%

MST373B - CLINICAL TRIALS (2023 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:3

Course Objectives/Course Description

 

This course is designed to train the students in the design and conduct of clinical trials and provide knowledge about the methods of statistical data analysis of clinical trials.

Course Outcome

CO1: Understand the study designs of randomized clinical trials

CO2: Apply statistical principles, concepts and methods for the analysis of data in clinical trials

CO3: Demonstrate competencies in evaluating clinical research data and communicating results

CO4: Demonstrate advanced critical thinking skills necessary to advance within the biopharmaceutical industry.

Unit-1
Teaching Hours:12
Introduction to Clinical Trials
 

Historical background of clinical trials - the need for clinical trials - ethics and planning of clinical trials - main features of study protocol - the selection of study subjects -treatment schedule - evaluation of patient response - follow-up studies -GCP/ICH guidelines

Unit-2
Teaching Hours:12
Phases of clinical trials
 

Different phases of clinical trials: phase I, phase II, phase III, phase IV - Basic study designs - randomized controlled trials - non-randomized concurrent controlled trials -historical controls - cross over design - withdrawal design - hybrid designs – group allocation designs and studies of equivalency.

Unit-3
Teaching Hours:12
Methods of randomization
 

Fixed allocation randomization - stratified randomization - adaptive randomization - unequal randomization - Intervention and placebos - blinding in clinical trials: unblended trials - single-blind trials - double- blind trials and triple-blind trials.

Unit-4
Teaching Hours:12
Estimation of sample size for clinical trials
 

Various methods for determining sample size for clinical trials: method for dichotomous response variable - continuous response variable - repeated measures – cluster randomization and equivalency of intervention - Multicenter trials.

Unit-5
Teaching Hours:12
Data management
 

Design of case report form - data collection - intention to treat analysis and per-protocol analysis - interim analysis - reporting adverse events - issues in data analysis - non- adherence - poor quality and missing data

Text Books And Reference Books:

1. Friedman, L.M., Furberg, C.D., DeMets David L., (2015), Fundamentals of Clinical Trials 5 th Edition, Springer.

2. Meinert Curtis L., (2012), Clinical Trials-Design, conduct and Analysis, 2 nd Edition Oxford University Press, New York.

Essential Reading / Recommended Reading

1. Remedica ( 2006), Clinical trials – A practical Guide to Design, Analysis and Reporting, Remedica Medical Education and Publishing.

2. Tom Brody (2016), Clinical Trials – Study Design, End points, Biomarkers, Drug safety, FDA and ICH guidelines.

3. Jo Ann Pfeiffer and Cris Wells (2017), A practical Guide to managing Clinical Trials, CRC Press, Taylor and Francis Group

Evaluation Pattern
Course Outcomes /Unit CAT1 45% CAT2 50% CAC1 50% Regular Program evaluations 45% ATTD 10 %
CO1 25 - 10 10 Not Applicable
CO2 20 10 15 15
CO3 - 20 20 15
CO4 - 20 5 5

 

MST373C - RELIABILITY ENGINEERING (2023 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:3

Course Objectives/Course Description

 

This course will provide knowledge in different probability models in the reliability evaluation of the system and its components. Reliability engineering is applied in the industry to reduce failures, ensure effective maintenance and optimize repair time.

Course Outcome

CO1: Demonstrate the understanding of basic concepts of reliability.

CO2: Analyze system reliability using probability models.

CO3: Evaluate reliability from the lifetime data using common estimation procedures

CO4: Create a stress-strength model for system reliability.

Unit-1
Teaching Hours:12
Basic concepts
 

Reliability of a system - failure rate - mean, variance and percentile residual life: identities connecting them - notions of ageing - IFR, IFRA, NBU, NBUE, DMRL, HNBUE, NBUC, etc. and their mutual implications - TTT transforms and characterization of ageing classes.

Practical Assignments:

1. Exercise on failure rate function and mrl function

2. Exercise on comparison ageing classes 

Unit-2
Teaching Hours:12
Lifetime models
 

Non-monotonic failure rates and mean residual life functions - study of lifetime models: exponential, Weibull, lognormal, generalized Pareto, gamma with reference to basic concepts and ageing characteristics - bathtub and upside-down bathtub failure rate distributions

Practical Assignments:

3. Exercise on exponential lifetime model

4. Exercise on Weibull lifetime model

5. Exercise on bathtub shaped lifetime model 

Unit-3
Teaching Hours:12
System reliability
 

Reliability systems with dependents components: Parallel and series systems, k out of n Systems - ageing properties with dependent and independents components - concepts and measures of dependence on reliability - RCSI, LCSD, PF2, WPQD.

Practical Assignments:

6. Exercise on reliability evaluation of series system

7. Exercise on reliability evaluation of a parallel system

8. Exercise on reliability evaluation of k out of n system

9. Exercise on reliability evaluation of dependent component system 

Unit-4
Teaching Hours:12
Reliability estimation
 

Reliability estimation using MLE: exponential, Weibull and gamma distributions based on censored and non-censored samples - UMVU estimation of reliability function - Bayesian reliability estimation of exponential and Weibull models

Practical Assignments:

10. Exercise on ML estimation under non-censored samples.

11. Exercise on ML estimation under censored samples.

12. Exercise on Bayesian estimation of reliability. 

Unit-5
Teaching Hours:12
Life testing
 

Life testing: basics – modelling lifetime – Accelerated Life Time (ALT) models- cumulative exposure models (CEM) - exponential CEM – stress-strength reliability – exponential stress-strength model.

Practical Assignments:

13. Exercise on basic life testing procedure.

14. Exercise on exponential CEM model.

15. Exercise on stress-strength reliability.

Text Books And Reference Books:

1.     Birolini, A. (2013). Reliability engineering: theory and practice. Springer Science & Business Media..

2.     Bain, L. (2017). Statistical analysis of reliability and life-testing models: theory and methods. Routledge.

Essential Reading / Recommended Reading
  1. Barlow, R. E., & Proschan, F. (1975). Statistical theory of reliability and life testing: probability models. Florida State Univ Tallahassee.
  2. Tobias, P. A., & Trindade, D. (2011). Applied reliability. CRC Press.
Evaluation Pattern

CIA 50%

ESE 50%

MST381 - RESEARCH - PROBLEM IDENTIFICATION AND FORMULATION (2023 Batch)

Total Teaching Hours for Semester:30
No of Lecture Hours/Week:3
Max Marks:50
Credits:1

Course Objectives/Course Description

 

This will equip the student to apply statistical methods they have studied in various courses

and present their work through research articles.

Course Outcome

CO1: Apply statistical techniques to a real-life problem.

CO2: Interpret and conclude the statistical analysis scientifically.

CO3: Present the work done through presentation and research article.

Unit-1
Teaching Hours:120
Problem Identification and Formulation
 

1.Research Problem Identification 

2.Formulation

Text Books And Reference Books:

For Dissertation/Project refer - Code of Research Conduct and Ethics:

https://kp.christuniversity.in/KnowledgePro/images/Regulations/CRCE.pdf

Essential Reading / Recommended Reading

Web Resources:

Research Articles from academic databases.

Evaluation Pattern

CIA-100%

 

MST431 - SURVIVAL ANALYSIS (2022 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course will provide an introduction to the principles and methods for the analysis of time-to-event data. This type of data occurs extensively in both observational and experimental biomedical and public health studies.

Course Outcome

CO1: Explore the fundamental concepts of survival models

CO2: Analyse survival data using various parametric models

CO3: Identify Non-Parametric Survival techniques for applications lifetime data

CO4: Demonstrate the understanding of various Competing Risks and their effects

Unit-1
Teaching Hours:12
Basic quantities and censoring
 

The hazard and survival functions - Mean residual life function - competing risk - right,left and interval censoring, truncation - likelihood for censored and truncated data - Parametric and non-parametric estimation in truncated and censored cases.

Practical Assignments:

1.Lab exercise on the parametric estimation of left and right-censored data

2.Lab exercise on the parametric estimation of truncated data

3.Lab exercise on the non-parametric estimation of censored and truncated data

Unit-2
Teaching Hours:12
Parametric Survival Models
 

Parametric forms and the distribution of log time - The exponential - Weibull - Gompertz - Gamma - Generalized Gamma - Coale-McNeil - and generalized F distributions - The U.S. life table - Approaches to modelling the effects of covariates - Parametric families - Proportional hazards models (PH) - Accelerated failure time models (AFT) - The intersection of PH and AFT. Proportional odds models (PO) - The intersection of PO and AFT - Recidivism in the U.S. 

Practical Assignments:

1.Lab exercise on parametric modelling pf survival data

2.Lab exercise on the proportional hazard model

3.Lab exercise on AFT models

 

Unit-3
Teaching Hours:12
Non-Parametric Survival Models
 

One-sample estimation with censored data - The Kaplan-Meier estimator - Greenwood's formula - The Nelson-Aalen estimator - The expectation of life - Comparison of several groups: Mantel- Haenszel and the log-rank test. 

Regression: Cox's model and partial likelihood - The score and information - The problem of ties - Tests of hypotheses - Time-varying covariates - Estimating the baseline survival - Martingale residuals.

Practical Assignments:

7.Lab exercise on Kaplan-Meier estimator and Nelson-Aalen estimator

8.Lab exercise on Mantel- Haenszel and the log-rank test

9.Lab exercise on the Cox model with time-varying covariate

Unit-4
Teaching Hours:12
Models for Discrete Data and Extensions
 

Cox's discrete logistic model and logistic regression - Modelling grouped continuous data and the complementary log-log transformation - Piece-wise constant hazards and Poisson regression - Current status data versus retrospective data - Open intervals and time since the last event - Backward recurrence times - Interval censoring. 

Practical Assignments:

10.Lab exercise on the discrete logistic model for survival data

11.Lab exercise on Poisson regression for survival data

12.Lab exercise on Piece-wise regression for survival data

Unit-5
Teaching Hours:12
Models for Competing Risks
 

Modelling multiple causes of failure - Research questions of interest - Cause-specific hazards - Overall survival - Cause-specific densities - Estimation: one-sample and the generalized Kaplan- Meier and Nelson-Aalen estimators - The Incidence function - Regression models - Weibull regression - Cox regression and partial likelihood - Piece-wise exponential survival and multinomial logits - The identification problem - Multivariate and marginal survival - The Fine-Gray model.

Practical Assignments:

13.Lab exercise on non-parametric modelling of competing risk data 

14.Lab exercise on parametric modelling of competing risk data

15.Lab exercise on multivariate survival data

Text Books And Reference Books:

1. Klein, J. P., & Moeschberger, M. L. (2006). Survival analysis: techniques for censored and truncated data. Springer Science & Business Media. 

2. Cleves, M.; W. G. Gould, and J. Marchenko (2016). An Introduction to Survival Analysis using Stata. Revised 3rd Ed. College Station, Texas: Stata Press. 

3. Kalbfleisch, J. D., & Prentice, R. L. (2011). The statistical analysis of failure time data,2nd Ed. John Wiley & Sons. 

4. Moore, D. F. (2016). Applied survival analysis using R. Switzerland: Springer. 

 

Essential Reading / Recommended Reading

1. Singer, J.D and J. B. Willett (2003) Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford, Oxford University Press.

2. Therneau, T. M. and P. M. Grambsch (2000). Modelling Survival Data: Extending the Cox Model, Springer, NY

3. Collett, D. (2015). Modelling survival data in medical research. Chapman and Hall/CRC.

4. Kalbfleisch, J. D., & Prentice, R. L. (2011). The statistical analysis of failure time data,2nd Ed. John Wiley & Sons.

5. Moore, D. F. (2016). Applied survival analysis using R. Switzerland: Springer.

Evaluation Pattern

CIA - 50%

ESE - 50%

 

MST432 - DESIGN AND ANALYSIS OF EXPERIMENTS (2022 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:4

Course Objectives/Course Description

 

 

This course will provide students with a mathematical background of various basic designs involving one-way and two-way elimination of heterogeneity and characterization properties. To prepare the students in deriving the expressions for analysis of experimental data and selection of appropriate designs in planning a scientific experimentation

Course Outcome

1: Demonstrate basic principles and characterization properties of various designs of the experiment.

2: Identify appropriate design of experiments to solve research problems of various domains.

3: Design factorial experiments with confounding.

4: Construct split and strip plot designs.

5: Analyse the Incomplete Block designs.

Unit-1
Teaching Hours:12
Basic of design of experiments
 

Basic principles of design of experiments - Randomization - Replication and Local control - Uniformity trials - Size and Shape of plots and blocks - Elements of linear estimation - Analysis of variance - Completely Randomized Design (CRD) - Randomized Complete Block Design (RCBD) and Latin Square Design (LSD) -  Missing plot techniques.

Unit-2
Teaching Hours:12
Analysis of Covariance
 

Analysis of covariance - Ancillary/Concomitant variable and study variable - Linear model for ANCOVA - Adjustment of treatment sum of squares in ANCOVA - One - Way and two-way classification with a single concomitant variable in CRD and RCBD designs.

Unit-3
Teaching Hours:12
Factorial experiments
 

Factorial experiments - Simple experiment (single factor) vs Factorial experiments - Mixed and Fixed factor experiments - Treatment combination in a factorial experiment - Simple effect - Main effect and Interaction effect in a factorial experiment - Yates method of computing factorial effects totals - Complete and partial confounding in symmetrical factorial experiments (22, 23, 33, 2nand 3n series) - Gain in the factorial experiments.

Unit-4
Teaching Hours:12
Plot and Strip - Plot designs
 

Split - Plot, Split - Split plot and Strip - Plot (Split Block) design - Situation for the usage of the design - Layout and analysis of the designs - Difference in the error components in the designs - Selection of factor for allocation in plots (main/sub) - Combined experiments -  Cross - Over designs.

Unit-5
Teaching Hours:12
Incomplete Block Designs
 

Balanced Incomplete Block (BIB) designs - General properties and Analysis with and without recovery of information - Construction of BIB designs - Parameter relationship - Intra and inter-block Analysis - Partially Balanced Incomplete Block Design (PBIBD) - Youden square designs - Lattice designs.

Text Books And Reference Books:

 

Montgomery, D.C. (2019). Design and Analysis of Experiments. John Wiley and Sons, Inc. New York

Essential Reading / Recommended Reading

 

 

1.Gupta, S.C and Kapoor, V.K. (2019). Fundamentals of Applied Statistics. 4th edition (Reprint). Sultan Chand and Sons. India.

2.Cochran, W.G. and Cox, G.M. (1992). Experimental Designs. John Wiley. 

3.Dean, A.M. and Voss, D. (1999). Design and Analysis of Experiments. Springer.

4.Das, M.N. and Giri, N.C. (1986). Design and Analysis of Experiments. New Age.

5.Lawson, J. (2015). Design and Analysis of Experiments with R. CRC Press

6.Dey, A. (1986). Theory of Block Designs. Wiley Eastern Ltd.

 

Evaluation Pattern

 

Component

Marks

CIA I

10

Mid Term Examination (CIA II)

25

CIA III

10

Attendance

05

End Trimester Exam

50

Total

100

MST433 - STOCHASTIC PROCESSES (2022 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:4

Course Objectives/Course Description

 

To equip the students with theoretical and practical knowledge of stochastic models which are used in economics, life sciences, engineering etc.

Course Outcome

By the end of the course, the learner will be able to:

CO1: List different stochastic models.

CO2: Identify ergodic Markov chains.

CO3: Analyse queuing models using continuous-time Markov chains.

CO4: Apply Brownian motion in finance problems.

 

Unit-1
Teaching Hours:12
Introduction
 

A sequence of random variables - definition and classification of the stochastic process - autoregressive processes and Strict Sense and Wide Sense stationary processes.

Unit-2
Teaching Hours:12
Discrete time Markov chains
 

Markov Chains: Definition, Examples - Transition probability matrix -  Chapman-Kolmogorv equation - classification of states - limiting and stationary distributions - ergodicity - discrete renewal equation and basic limit theorem - Absorption probabilities - Criteria for recurrence - Generic application: hidden Markov models.

Unit-3
Teaching Hours:12
Continuous time Markov chains and Poisson process
 

Transition probability function - Kolmogorov differential equations - Poisson process: homogenous process, inter-arrival time distribution, compound process - Birth and death process - Service applications: Queuing models- Markovian models.

Unit-4
Teaching Hours:12
Branching process
 

Galton-Watson branching processes - Generating function - Extinction probabilities - Continuous-time branching processes - Extinction probabilities - Branching processes with general variable lifetime.

Unit-5
Teaching Hours:12
Renewal process and Brownian motion
 

Renewal equation - Renewal theorem - Generalisations and variations of renewal processes -  Brownian motion - Introduction to Markov renewal processes.

Text Books And Reference Books:

1.Karlin, S. and Taylor, H.M. (2014). A first course in stochastic processes. Academic Press.

2.S. M. Ross (2014). Introduction to Probability Models. Elsevier.

 

Essential Reading / Recommended Reading

 

  1. Feller, W. (2008) An Introduction to Probability Theory and its Applications, Volume I&II , 3rd Ed., Wiley Eastern.
  2. J. Medhi (2009) Stochastic Processes, 3rd Edition, New Age International.
  3. Dobrow, R.P. (2016), Introduction to Stochastic Processes with R, Wiley Eastern.
  4. Cinlar, E. (2013). Introduction to stochastic processes. Courier Corporation.

 

Evaluation Pattern

Component

Marks

CIA I

10

Mid Semester Examination (CIA II)

25

CIA III

10

Attendance

05

End Semester Exam

50

Total

100

MST471A - NEURAL NETWORKS AND DEEP LEARNING (2022 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

 

The objective of this course is to provide fundamental knowledge of neural networks and deep learning. This course gives a brief idea of the basics of neural networks, shallow and deep neural networks and other methods to build various research projects. 

Course Outcome

1: Identify the difference between biological and arithmetic neural networks.

2: Demonstrate the different types of supervised learning algorithms.

3: Build and train various Convolution Neural Networks.

4: Implement Recurrent Neural Networks and other artificial neural networks for real-time applications.

Unit-1
Teaching Hours:15
Introduction to Artificial Neural Networks
 

 

Fundamental concepts of Artificial Neural Networks (ANN) - Biological neural networks - Comparison between biological neuron and artificial neuron - Evolution of neural networks - Scope and limitations of ANN - Basic models of ANN - Learning methods - Activation functions - Important terminologies of ANN: Weights - Bias - Threshold - Learning Rate - Momentum factor - Vigilance parameters.

Unit-2
Teaching Hours:15
Supervised Learning Algorithms
 

 

Concept of supervised learning algorithms - Perceptron networks - Adaptive linear neuron (Adaline) - Multiple adaptive linear neuron - Back-Propagation network: Learning factors - Initial weights - Learning rate ɑ - Momentum factor - Generalization - Training and testing of the data.

Unit-3
Teaching Hours:15
Unsupervised Learning Algorithms
 

 

Concept of unsupervised learning algorithms - Fixed weight competitive net: Maxnet - Mexican Hat net - Hamming networks - Kohonen self-organizing feature maps - Learning vector quantization.

Unit-4
Teaching Hours:15
Convolution Neural Networks
 

 

Introduction - Components of Convolution Neural Networks (CNN) architecture: Padding - Strides - Rectified linear unit layer - Exponential linear unit - Pooling - Fully connected layers  - Local response normalization - Hierarchical feature engineering -  Training CNN using Backpropagation through convolutions - Case studies: AlexNet - GoogLeNet.

Unit-5
Teaching Hours:15
Deep Reinforcement Learning
 

 

Stateless algorithms: Naive algorithms - Upper bounding methods - Simple reinforcement learning for Tic-Tac-Toe - Straw-Man algorithms - Bootstrapping for value function learning - One policy versus off policy methods: SARSA - Policy gradient methods: Finite difference method - Likelihood ratio method - Monte Carlo tree search. 

Text Books And Reference Books:

Charu C. Aggarwal (2018) Neural Networks and Deep Learning A Textbook, Springer International Publishing, Switzerland.

Essential Reading / Recommended Reading
  1. S.N Sivanandam, S.N Deepa (2018). Principles of soft computing. Wiley India.
  2. S Lovelyn Rose, L Ashok Kumar, Karthika Renuka (2019). Deep Learning using Python. Wiley India. 
  3. Francois Chollet (2017). Deep Learning with Python. Manning Publishing.
  4. Andreas C. Muller & Sarah Guido (2017). Introduction to Machine Learning with Python. O’Reilly Media, Inc.
Evaluation Pattern

CIA-50%

ESE-50%

MST471B - STATISTICAL GENETICS (2022 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

To enable the students to understand and apply different concepts of statistical genetics in large populations with selection, mutation and migration. The students would be exposed to the physical basis of inheritance, detection and estimation of linkage, estimation of genetic parameters and development of selection indices.

Course Outcome

CO1: Describe basic concepts of estimation of linkage and segregation in large populations.

CO2: Demonstrate the effect of systematic forces on change of gene frequency.

CO3: Apply statistical methodology to estimate the correlation between relatives and selection index.

CO4: Interpret the results of various statistical genetics techniques.

CO5: Estimate genetic variance and analyse its partitioning.

Unit-1
Teaching Hours:15
Segregation and Linkage
 

Physical basis of inheritance - Analysis of segregation - Detection and Estimation of linkage for qualitative characters - Amount of information about linkage - Combined estimation - Disturbed segregation.

Practical Assignments:

1.      Analysis of segregation, detection and estimation of linkage.

2.      Estimation of Amount of information about linkage.

3.      Calculation of combined estimationof linkage.

Unit-2
Teaching Hours:15
Equilibrium law and Sex-Linked gene
 

Gene and genotypic frequencies - Random mating and Hardy-Weinberg law - Application and extension of the equilibrium law - Fisher’s fundamental theorem of natural selection - Disequilibrium due to linkage for two pairs of genes - Sex - Linked genes.

Practical Assignments:

4. Estimation of disequilibrium due to linkage for two pairs of genes.

5. Estimation of path coefficients.

6. Estimation of equilibrium between forces in large populations.

Unit-3
Teaching Hours:15
Systematic forces
 

Forces affecting gene frequency: Selection - Mutation and Migration - Equilibrium between forces in large populations - Polymorphism.

Practical Assignments:

7. Estimation of changes in gene frequency due to systematic forces.

8. Estimation of the Inbreeding coefficient.

Unit-4
Teaching Hours:15
Genetic variance and its partitioning
 

Polygenic system for quantitative characters - Concepts of breeding value and Dominance deviation - Genetic variance and its partitioning.

Practical Assignments:

 9. Analysis of genetic components of variation.

10. Estimation of breeding values.

Unit-5
Teaching Hours:15
Association and Selection index
 

Correlation between relatives – Heritability - Repeatability and Genetic correlation - Response due to selection - Selection index and its applications in plants and animals improvement Programme - Correlated response to selection - Restricted selection index - Inbreeding and crossbreeding - Changes in mean and variance.

Practical Assignments:

11. Estimation of Heritability and repeatability coefficient,

12. Estimation of the genetic correlation coefficient.

Text Books And Reference Books:

1. Jain, J.P. (2017). Statistical Techniques in Quantitative Genetics. Tata McGraw

Essential Reading / Recommended Reading

1. Laird N.M and Christoph, L. (2011). The Fundamental of Modern Statistical Genetics. Springer.

2. Balding DJ, Bishop, M. and Cannings, C. (2001). Handbook of Statistical Genetics. John Wiley.

3. Shizhong Xu.(2013). Principles of Statistical Genomics. Springer.

4.Falconer, D.S. (2009). Introduction to Quantitative Genetics. English Language Book Society. Longman. Essex.

Evaluation Pattern

CIA - 50 %

ESE- 50 %

MST471C - ACTUARIAL METHODS (2022 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course is designed to equip students with the knowledge of actuarial models and their applications

Course Outcome

CO1: Demonstrate the understanding of basic concepts of actuarial methods.

CO2: Identify various actuarial models.

CO3: Illustrate survival models and life tables.

CO4: Interpret the real-life data based on exploratory data analysis.

CO5: Apply actuarial models to real-life data.

Unit-1
Teaching Hours:15
Introduction to actuarial statistics
 

Utility theory-introduction - insurance and utility theory - models for individual claims and their sums - curtate future lifetime - the force of mortality - assumptions for fractional ages - some analytical laws of mortality - multiple life functions - joint life and last survivor status - insurance and annuity benefits through multiple life functions - evaluation for special mortality laws.

 

 Practical Assignments:

               1.      Problems based on multiple life functions

               2.   Illustrate discrete and continuous annuity benefits

Unit-2
Teaching Hours:15
Survival analysis and life tables
 

Introduction to survival analysis - life table and its relation with survival function - examples - assumptions for fractional ages - estimate empirical survival and loss distribution using Kaplan-Meier estimator - Nelson Aalen estimator - Cox proportional hazards and Kernel density estimators.

 

Practical Assignments:

             3. Apply survival models to simple problems in long-term insurance, pensions and banking.

             4. Preparation of life tables based on the real life data.

             5. Estimation of survival distribution using Kaplan-Meier estimator, Nelson Aalen estimator, Cox proportional hazards and Kernel density estimators

Unit-3
Teaching Hours:15
Actuarial models
 

Principles of actuarial modelling - stochastic and deterministic models - their advantages and disadvantages - frequency models: distributions suitable for modelling frequency of losses (Poisson, Binomial, negative binomial and geometric distributions) - fundamentals of aggregate models - computation of aggregate claims distributions and calculation of loss probabilities - evaluate the effect of coverage modifications (deductibles, limits and coinsurance) - inflation on aggregate models.

Practical Assignments:

6. Compute relevant moments, probabilities and other distributional quantities for collective risk models.

7. Compute aggregate claims, distributions and use them to calculate loss probabilities.

8. Evaluate the effect of coverage modifications and inflation on aggregate models.

Unit-4
Teaching Hours:15
Insurance and Annuities
 

Principles of compound interest -Nominal and effective rates of interest and discount - the force of interest and discount - compound interest - accumulation factor - continuous - compounding - life insurance - life annuities - net premiums - net premium reserves - some practical considerations - premiums that include expenses - general expenses - types of expenses - per policy expenses - claim amount distributions - approximating the individual model - stop-loss insurance.

 

 

Practical Assignments:

 

9.      Illustrate discrete and continuous insurance benefits

10.      Illustrate discrete and continuous annuity benefits

Unit-5
Teaching Hours:15
Data and Systems
 

Data as a resource for problem-solving - exploratory data analysis: single and multiple linear regression - principal component analysis and survival analysis - statistical learning: difference between supervised and unsupervised learning - professional and risk management issues - ethical and regulatory issues involved in using personal data and extremely large data sets - visualizing data and reporting.

 

Practical Assignments:

11.      Apply principal component analysis to reduce the dimensionality of a complex data set.

12.      Fit a simple and multiple linear models to a data set and interpret the results.

13.      Fit a survival model to a data set and interpret the output.

Text Books And Reference Books:
  1. N.L. Bowers, H.U. Gerber, J.C. Hickman, D.A. Jones and C.J. Nesbitt, (2014), ‘Actuarial Mathematics’, Society of Actuaries, Ithaca, Illinois, U.S.A.
Essential Reading / Recommended Reading

1.         Zdzislaw Brzezniak and Tomasz Zastawniak (2000), Basic stochastic processes: A course through exercises. Springer.

2.         Grimmett Geoffery and David Stizaker (2001), Probability and random processes. Oxford University Press.

3.         J. Medhi, Stochastic Processes (2009), John Wiley.

Evaluation Pattern

CIA 50%

ESE 50%

MST481 - RESEARCH MODELING (2022 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:50
Credits:2

Course Objectives/Course Description

 

This will equip the student to apply statistical methods they have studied in various courses and present their work through research articles.

Course Outcome

By the end of the course, the learner will be able to

CO1: Apply statistical techniques to a real-life problem.

CO3: Interpret and conclude the statistical analysis scientifically.

CO4: Present the work done through presentation and research article. 

Unit-1
Teaching Hours:60
Modelling
 

1. Apply various statistical methods in solving a real-life problem.

2. Comparison with the existing models or results.

 

Text Books And Reference Books:

_

Essential Reading / Recommended Reading

-

Evaluation Pattern

CIA 50%

ESE 50%

MST482 - SEMINAR PRESENTATION (2022 Batch)

Total Teaching Hours for Semester:30
No of Lecture Hours/Week:3
Max Marks:50
Credits:1

Course Objectives/Course Description

 

This course is to enhance the verbal and written presentation skills of students and to develop analytical skills as students learn new areas and ideas in Statistics. 

Course Outcome

By the end of the course, the learner will be able to,

CO1: Demonstrate presentation and writing skills.

 

Unit-1
Teaching Hours:30
Presentation
 

1. Prepare a report on a relevant topic.

2. Present it well before the class and panel members.

 

Text Books And Reference Books:

_

Essential Reading / Recommended Reading

-

Evaluation Pattern

CIA 50%

ESE 50%

MST531 - STATISTICAL QUALITY CONTROL (2022 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course provides an introduction to the application of statistical tools in the industrial environment to study, analyze and control the quality of products.

Course Outcome

CO1: Demonstrate the concepts of point and interval estimation of unknown parameters and their significance using large and small samples.

CO2: Apply the idea of sampling distributions of difference statistics in testing of hypotheses.

CO3: Infer the concept of nonparametric tests for single sample and two samples.

Unit-1
Teaching Hours:12
Statistical Process Control
 

 

Meaning and scope of statistical quality control - Causes of quality variation - Control charts for variables and attributes - Rational subgroups - Construction and operation of, σ, R, np, p, c and u charts - Operating characteristic curves of control charts. Process capability analysis using histogram, probability plotting and control chart - Process capability ratios and their interpretations.

Unit-2
Teaching Hours:12
Advanced Control Charts
 

Specification limits and tolerance limits - Modified control charts - Basic principles and design of cumulative - sum control charts – Concept of V-mask procedure – Tabular CUSUM charts - Construction of Moving range - moving-average and geometric moving-average control charts.

Unit-3
Teaching Hours:12
Attribute sampling plans
 

Acceptance sampling: Sampling inspection by attributes – single, double and multiple sampling plans – Rectifying Inspection - Measures of performance: OC, ASN, ATI and AOQ functions - Concepts of AQL, LTPD and IQL - Dodge – Romig and MIL-STD-105D tables

 

Unit-4
Teaching Hours:12
Variables Sampling Plans
 

 

 Sampling inspection by variables - known and unknown sigma variables sampling plan - Merits and limitations of variables sampling plan - single, double and multiple sampling plans - Derivation of OC curve – determination of plan parameters.

Unit-5
Teaching Hours:12
Continuous and Cumulative Sampling Plans
 

 Continuous Sampling Plans (CSP): CSP-1- CSP-2 - CSP-3 - Skip-Lot Sampling Plans (SkSP): SkSP-1 - SkSP-2  with SSP as reference plan - Chain Sampling Plans (ChSP - 1) with SSP as reference plan - Tighten-Normal-Tighted (TNT) sampling plan with SSP as reference plan– Decision Lines.

Text Books And Reference Books:

[1]. Stochastic Processes, R.G Gallager, Cambridge University Press, 2013.

[2]. Stochastic Processes, S.M Ross, Wiley India Pvt. Ltd, 2008.

Essential Reading / Recommended Reading

1. Juran, J.M., and De Feo, J.A. (2010). Juran’s Quality control Handbook – The Complete Guide to Performance Excellence, Sixth Edition, Tata McGraw-Hill, New Delhi.

    

2. Schilling, E. G., and Nuebauer, D.V. (2009). Acceptance Sampling in Quality Control, Second Edition, CRC Press, New York.

 

3. Duncan, A. J. (2003.). Quality Control and Industrial Statistics, Irwin-Illinois, US.

Evaluation Pattern

CIA - 50%

ESE - 50%

MST532 - MULTIVARIATE ANALYSIS (2022 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:5
Max Marks:100
Credits:4

Course Objectives/Course Description

 

The exposure provided to the multivariate data structure, multinomial and multivariate normal distribution, estimation and testing of parameters, various data reduction methods would help the students in having a better understanding of research data, its presentation and analysis. This course helps to understand multivariate data analysis methods and their applications in various research areas.

Course Outcome

CO1: Describe concepts of multivariate normal distribution.

CO2: Demonstrate the concepts of MANOVA and MANCOVA.

CO3: Identify various classification methods for multivariate data.

CO4: Analyze various data reduction methods for the multivariate data structure.

CO5: Interpret the results of various multivariate methods.

Unit-1
Teaching Hours:12
Multivariate Distributions
 

Basic concepts on multivariate variables - Multivariate normal distribution - Marginal and conditional distribution - Concept of random vector - Its expectation and Variance - Covariance matrix. Marginal and joint distributions - Conditional distributions and Independence of random vectors - Multinomial distribution - Characteristic functions in higher dimensions - Multiple regressions and multiple correlations - Partial regression and Partial correlation (illustrative examples).

Unit-2
Teaching Hours:12
MANOVA and MANCOVA
 

Multivariate analysis of variance (MANOVA) and Covariance (MANCOVA) of one and two-way classified data with their interactions - Univariate and Multivariate Two-Way Fixed-effects Model with Interaction.

Unit-3
Teaching Hours:12
Equality of Mean and Variance Vector
 

Wishart distribution (definition, properties) - Construction of tests - Union - Intersection and likelihood ratio principles - Inference on mean vector - Hotelling's T2- Comparing Mean Vectors from Two Populations - Bartlett’s Test. 

Unit-4
Teaching Hours:12
Classification and Discriminant Procedures
 

Concepts of discriminant analysis - Computation of linear discriminant function (LDF) - Classification between k multivariate normal populations based on LDF - Fisher’s Method for discriminating two or several populations - Evaluating Classification Functions - Probabilities of misclassification and their estimation - Mahalanobis D2.

Unit-5
Teaching Hours:12
Factor Analysis and Cluster Analysis
 

Factor analysis: - Orthogonal factor model - Factor loadings - Estimation of factor loadings - Factor scores and Its applications.

Cluster Analysis: - Distances and similarity measures - Hierarchical clustering methods - K- Means method. 

 

Text Books And Reference Books:

1. Anderson, T.W. (2004). An Introduction to Multivariate Statistical Analysis. John

Wiley. New York.

2. Johnson, R.A. and Wichern, D.W. (2018). Applied Multivariate Statistical Analysis.

6th edn. Prentice- Hall. London.

 

Essential Reading / Recommended Reading

1. Rohatgi, V.K. and Saleh, A.K.M.E. (2015). An Introduction to Probability Theory and

Mathematical Statistics. 2nd edn. John Wiley & Sons. New York.

2. Srivastava, M.S. and Khatri, C.G. (1979). An Introduction to Multivariate Statistics.

North Holland.

3. Muirhead, R.J. (1982). Aspects of Multivariate Statistical Theory. John Wiley. New

York.

Evaluation Pattern

 

CIA-50%

ESE-50%

MST571A - BIG DATA ANALYTICS (2022 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course has been designed to train the students in handling different types of Big data sets and provide knowledge about the methods of handling these types of data sets.  

Course Outcome

CO1: Demonstrate an understanding of basic concepts of Big data

CO2: Identify different types of Hadoop architecture

CO3: Illustrate the parallel processing of data using MapReduce techniques

CO4: Analyze the Big data under Spark architecture

CO5: Demonstrate the programming of Big data using Hive and Pig environments

Unit-1
Teaching Hours:15
Introduction
 

Concepts of Data Analytics: Descriptive, Diagnostic, Predictive, Prescriptive analytics -Big Data characteristics: Volume, Velocity, Variety, Veracity of data - Types of data: Structured, Unstructured, Semi-Structured, Metadata - Big data sources: Human-Human communication, Human-Machine Communication, Machine-Machine Communication - Data Ownership - Data Privacy.

Practical Assignments:

1. Setting up infrastructure and Automation environment

2. Case study for identifying Data Characteristics

Unit-2
Teaching Hours:15
Big Data Architecture
 

 

Standard Big data architecture - Big data application - Hadoop framework - HDFS Design goal - Master-Slave architecture - Block System - Read-write Process for data - Installing HDFS - Executing in HDFS: Reading and writing Local files and Data streams into HDFS - Types of files in HDFS - Strengths and alternatives of HDFS - Concept of YARN.

 

Practical Assignments:

3.  Exercise on Installing HDFS

4.  Exercise on Reading and Writing Local files into HDFS

5.  Exercise on Reading and Writing Data streams into HDFS

 

 

Unit-3
Teaching Hours:15
Parallel Processing with MapReduce
 

Introduction to MapReduce - Sample MapReduce application: Wordcount - MapReduce Data types and Formats - Writing MapReduce Programming - Testing MapReduce Programs - MapReduce Job Execution - Shuffle and Sort - Managing Failures - Progress and Status Updates.

Practical Assignments:

6. Exercise on MapReduce applications

7. Exercise on writing and testing MapReduce Programs

8. Exercise on Shuffle and Sort

9. Exercise on Managing Failures

Unit-4
Teaching Hours:15
Stream Processing with Spark
 

Stream processing Models and Tools - Apache Spark - Spark Architecture: Resilient Distributed Datasets, Directed Acyclic Graph - Spark Ecosystem - Spark for Big Data Processing: MLlib, Spark GraphX, SparkR, SparkSQL, Spark Streaming - Spark versus Hadoop

Practical Assignments:

10. Exercise on installing Spark

11. Exercise on Directed Acyclic Graph

12. Exercise on Spark using MLlib, Spark GraphX

13. Exercise on Spark using SparkR, Spark Streaming

Unit-5
Teaching Hours:15
Hive and Pig
 

 

Hive Architecture - Components - Data Definition - Partitioning - Data Manipulation - Joins, Views and Indexes - Hive Execution - Pig Architecture - Pig Latin Data Model - Latin Operators - Loading Data - Diagnostic Operators - Group Operators - Pig Joins - Row Level Operators - Pig Built-in function - User-defined functions - Pig Scripts.

Practical Assignments:

14. Exercise on Hive Architecture

15. Exercise on Pig Architecture

 

Text Books And Reference Books:
  1. Anil Maheshwari (2020). Big Data. 2nd Edition. McGraw Hill Education Pvt Ltd.
Essential Reading / Recommended Reading
  1. Thomas Erl, Wajid Khattak and Paul Buhler (2016). Big Data Fundamentals: Concepts, Drivers and Techniques. Service Tech Press.
  2. Julián Luengo, Diego García-Gil, Sergio Ramírez-Gallego, Salvador García, Francisco Herrera (2020). Big Data Preprocessing: Enabling Smart Data. Springer Nature Publishing.

        3.Seema Acharya, Subhasini Chellappan (2019), Big Data and Analytics. 2nd Edition, Wiley India Pvt Ltd.

Evaluation Pattern

CIA - 50%

ESE - 50%

MST571B - DEMOGRAPHY AND VITAL STATISTICS (2022 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:04

Course Objectives/Course Description

 

This course has been designed to train students in the applications of statistics in demographic studies

Course Outcome

CO1: Demonstrate a solid understanding of key demographic concepts and measures

CO2: Understand the factors influencing these dynamics and interpret their implications.

CO3: Develop practical skills in collecting, processing, and analyzing demographic data

CO4: Evaluate population policies and their impacts on social, economic, and health outcomes

Unit-1
Teaching Hours:15
Introduction
 

Definition and scope of demography -Importance of demographic analysis - Sources of demographic data - census, registration, ad-hoc surveys - Hospital records - Demographic profiles of the Indian Census

Practical Assignments:

 

  1. Case study for demographic data
Unit-2
Teaching Hours:15
Life Tables
 

Complete life table and its main features - Uses of life table - Makehams and Gompertz curves - National life tables - UN model life tables - Abridged life tables - Stable and stationary populations.

Practical Assignments:

2.Exercise on lifetables

3.Exercise on Makehams and Gompertz curves

4.Exercise on abridged life tables

 

Unit-3
Teaching Hours:15
Measurement of Fertility
 

Crude birth rate - General fertility rate - Age-specific birth rate - Total fertility rate - Gross reproduction rate - Net reproduction rate.

Unit-4
Teaching Hours:15
Measurement of Mortality
 

Crude death rate - Standardized death rates - Age-specific death rates - Infant Mortality rate - Death rate by cause.

Practical Assignments:

 

  1. Exercise on standardised death rates
  2. Exercise on death rate by cause
Unit-5
Teaching Hours:15
Migration Models
 

Internal migration and its measurement - migration models - concept of international migration - Net migration - International and postcensal estimates - Projection method including logistic curve fitting - Decennial population census in India.

Practical Assignments:

  1. Exercise on International and postcensal estimates

Exercise on Projection method

Text Books And Reference Books:

1.      Whipple, G. C. (2018). Vital statistics; an introduction to the science of demography. Wiley. 

Essential Reading / Recommended Reading
  1. Alho, J. M., & Spencer, B. D. (2005). Statistical demography and forecasting . New York: Springer.
Evaluation Pattern

CIA50%

ESE50%

MST571C - RISK MODELLING (2022 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course will equip students with a wide variety of statistical methods for modelling risk.

Course Outcome

CO1: Demonstrate an understanding of basic concepts of risk modelling.

CO2: Apply probabilistic concepts for modelling risk.

CO3: Analyse risk using statistical dose-response models.

CO4: Apply risk management to individual portfolio problems

Unit-1
Teaching Hours:12
Basic Risk Models
 

Distinguishing Characteristics Of Risk Analysis - Traditional Health Risk Analysis - Defining Risks: Source, Target, Effect, Mechanism - Basic Quantitative Risk Models - Risk as Probability of a Binary Event - Hazard Rate Models

Practical Assignments:

1. Lab exercise on the quantitative risk model.

2.. Lab exercise on the hazard rate model

Unit-2
Teaching Hours:18
Risk Assessment Modelling
 

Conditional Probability Framework for Risk Calculations - Population Risks Modeled by Conditional Probabilities - Trees, Risks and Martingales - Compartmental Flow Simulation Models - Monte Carlo Uncertainty Analysis - Introduction to Exposure Assessment - Uncertainty Analysis

Practical Assignments:

3.  Lab exercise on risk calculations.

4.  Lab exercise on risk modelling by conditional probabilities.

5. Lab exercise on  compartment flow simulation model.

6. Lab exercise on  Monte Carlo uncertainty analysis

Unit-3
Teaching Hours:15
Advanced Statistical Risk Modelling
 

Statistical Dose-Response Modeling - Exposure and Response Variables - Risk, Confidence Limits, and Model Fit - Model Uncertainty and Variable Selection - Dealing with Missing Data

 

Practical Assignments:

7.  Lab exercise on Dose-Response modelling.

8. Lab exercise on the estimation of risk and confidence limit.

9. Lab exercise on variable selection procedures.

10. Lab exercise on missing data algorithms

Unit-4
Teaching Hours:17
Causality
 

Statistical vs Causal Risk Modeling - Criteria for Causation - Epidemiological Criteria for Causation - Criteria for Inferring Probable Causation - Causal Graph Models and Knowledge Representation - Testing Hypothesized Causal Graph Structures - Causal Graphs in Risk Analysis - Probabilistic Inferences in DAG Models - Using DAG Models to Make Predictions

Practical Assignments:

11.  Lab exercise on causal risk models.

12. Lab exercise on causal graph models.

13. Lab exercise on Testing Hypothesized Causal Graph Structures.

14. Lab exercise on DAG models

 

 

Unit-5
Teaching Hours:13
Individual Risk Management Decisions
 

Value Functions and Risk Profiles - Rational Individual Risk-Management via Expected Utility - EU Decision-Modeling Basics - Decision-Making Algorithms and Technologies - Axioms for EU Theories - Cognitive Heuristics and Biases Violate Reduction - Subjective Probability and Subjective Expected Utility (SEU)

Practical Assignments:

15. Lab exercise on EU decision modelling.

16. Lab exercise on optimization of decision-making algorithms

Text Books And Reference Books:
  1. Cox Jr, L. A. (2012). Risk analysis foundations, models, and methods. Springer Science & Business Media.
Essential Reading / Recommended Reading
  1. Pfaff, B. (2016). Financial risk modelling and portfolio optimization with R. John Wiley & Sons. Müller, A. C., & Guido, S. (2016). Introduction to machine learning with Python: a guide for data scientists. “O’Reilly Media, Inc."
  2. Gray, R. J., & Pitts, S. M. (2012). Risk modelling in general insurance: From principles to practice. Cambridge University Press.
  3. De Rocquigny, E. (2012). Modelling under risk and uncertainty: an introduction to statistical, phenomenological and computational methods. John Wiley & Sons.

 

Evaluation Pattern

CIA - 50%

ESE - 50%

MST572A - BAYESIAN STATISTICS (2022 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

Students who complete this course will gain a solid foundation in how to apply and understand Bayesian statistics and how to understand Bayesian methods vs frequentist methods.  Topics covered include: an introduction to Bayesian concepts; Bayesian inference for binomial proportions, Poisson means, and normal means; modelling

Course Outcome

CO1: Identify Bayesian methods for a binomial proportion and a Poisson mean

CO2: Perform Bayesian analysis for differences in proportions and means

CO3: Analyse normal distributed data in the Bayesian framework

CO4: Evaluate posterior distribution using various sampling procedures.

CO5: Compare Bayesian methods and frequentist methods.

Unit-1
Teaching Hours:15
Introduction to Bayesian Thinking
 

Basics of minimaxity - subjective and frequentist probability - Bayesian inference -  prior distributions - posterior distributions -  loss function - the principle of minimum expected posterior loss - quadratic and other common loss functions - advantages of being Bayesian - Improper priors - common problems of Bayesian inference - Point estimators - Bayesian confidence intervals, testing - credible intervals                                                                                       

Practical Assignments:                                                                 

  1. Construction of prior, conditional and posterior probabilities for the chosen data set
  2. Computation minimum expected posterior loss.
  3. Computation of Bayesian confidence intervals.
Unit-2
Teaching Hours:15
Bayesian Inference for Discrete Random Variables
 

Two Equivalent Ways of Using Bayes' Theorem - Bayes' Theorem for Binomial with Discrete Prior - Important Consequences of Bayes' Theorem - and Bayes' Theorem for Poisson with Discrete prior.                                                        

Practical Assignments:                                                     

  1. Bayes Classification
  2. Examples on Binomial distribution with discrete prior.
  3. Examples of Poisson distribution with discrete prior.
Unit-3
Teaching Hours:15
Bayesian Inference for Binomial Proportion
 

Using a Uniform Prior - Using a Beta Prior - Choosing Your Prior - Summarizing the Posterior Distribution - Estimating the Proportion - Bayesian Credible Interval

Comparing Bayesian and Frequentist Inferences for Proportion :

Frequentist Interpretation of Probability and Parameters - Point Estimation -  Comparing Estimators for Proportion - Interval Estimation - Hypothesis Testing - Testing a One-Sided Hypothesis - Testing a Two-Sided Hypothesis.                Bayesian Inference for Poisson: Some Prior Distributions for Poisson - Inference for Poisson Parameter.                       

Practical Assignments:                                                                 

  1. Estimation of  binomial proportion using uniform prior distribution.
  2. Estimation of binomial proportion using beta prior  distribution.
  3. Estimation of Poisson parameter using some prior distributions
Unit-4
Teaching Hours:15
Bayesian Inference for Normal Mean
 

Bayes' Theorem for Normal Mean with a Discrete Prior - Bayes' Theorem for Normal Mean with a Continuous Prior - Normal Prior, Bayesian Credible Interval for Normal Mean - Predictive Density for Next Observation.        

Practical Assignments:     

  1. Bayes estimator for Normal Mean with a Discrete Prior.
  2. Bayes estimator for Normal Mean with a Continuous Prior.
  3. Bayes Credible interval for the normal mean.
Unit-5
Teaching Hours:15
Bayesian Computations
 

Analytic approximation - E-M Algorithm - Monte Carlo sampling - Markov Chain Monte Carlo Methods - Metropolis-Hastings Algorithm - Gibbs sampling: examples and convergence issues.                                     

Practical Assignments:     

  1. E-M algorithm.
  2. Monte-Carlo sampling.
  3. Gibbs Sampling.
  4. Markov Chain Monte-Carlo application.
Text Books And Reference Books:

1. Bolstad W. M. and Curran, J.M. (2016) Introduction to Bayesian Statistics 3rd Edition.   Wiley, New York

2.  Jim, A. (2009). Bayesian Computation with R, 2nd Edition, Springer.

Essential Reading / Recommended Reading
  1. Berger, J.O. (1985a). Statistical Decision Theory and Bayesian Analysis, 2nd Ed. Springer-Verlag, New York.
  2. Christensen R, Johnson, W., Branscum, A. and Hanson T. E. (2011). Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians, Chapman & Hall.
  3. Congdon, P. (2006). Bayesian Statistical Modeling, Wiley
  4. Ghosh, J. K., Delampady M. and T. Samantha (2006). An Introduction to Bayesian Analysis: Theory & Methods, Springer.
  5. Rao. C.R. and Day. D. (2006). Bayesian Thinking, Modeling & Computation, Handbook of Statistics, Vol. 25. Elsevier.

 

Evaluation Pattern

CIA 50% 

ESE 50%

MST572B - SPATIAL STATISTICS (2022 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course has been conceptualized in order to understand the fundamental and applied concepts of spatial statistics that describe the diverse set of methods to model and analyze the various types of Spatial data. 

Course Outcome

CO1: Demonstrate an understanding of the fundamental concepts of spatial statistical analysis.

CO2: Identify the various types of spatial data by plots.

CO3: Apply the appropriate statistical model to the various types of spatial data.

CO4: Analyze and interpret the spatial data problems of various disciplines.

Unit-1
Teaching Hours:15
Introduction to spatial statistics
 

Spatial data - Types of spatial data- Geostatistical data, Lattice data, Point pattern data with examples  - Visualizing spatial data: Traditional plots, lattice plots and interactive plots – Exploratory spatial data analysis - Intrinsic stationarity, Square-Root-Differences Cloud -  The Pocket plot – Decomposing the data into large and small scale variation -  Analysis of residuals – Variogram of residuals.

Practical Assignments:

1.     Exercise on the visualization of spatial data using traditional plots,

2.     Exercise on the visualization of spatial data using lattice and interactive plots

 

3.     Exercise on exploratory data analysis

Unit-2
Teaching Hours:15
Geostatistical data
 

Stationary Processes: Variogram, Covariogram and Correlogram - Estimation of variogram: Comparison of the variogram and covariogram estimation, exact distribution theory of the variogram - Robust estimation of variogram –  Spectral representations: Valid covariograms and variograms - Variogram model fitting: Criteria for fitting a variogram model, properties of variogram-parameter estimators, Cross-validating the fitted variogram.

Practical Assignments:

4.     Exercise on exploratory variogram analysis

5.     Exercise on variogram

6.     Exercise on variogram modelling

 

7.     Exercise on residual variogram modelling 

Unit-3
Teaching Hours:15
Spatial prediction and kriging
 

Scale of variation -  Ordinary Kriging: Effect of variogram parameters on Kriging,  Lognormal and Trans-Gaussian Kriging, Cokriging – Robust Kriging – Universal Kriging : Estimation of variogram for Universal Kriging – Median-Polish Kriging: Gridded and non-gridded data, Median Polishing spatial data, Bias in Median-Based  covariogram estimators – Applications of Geostatistics.

Practical Assignments:

8.     Exercise on Ordinary Kriging

9.     Exercise on Robust Kriging

 

10.     Exercise on Universal Kriging

Unit-4
Teaching Hours:15
Spatial models on lattice data
 

Lattices – Spatial data analysis, Trend removal -  Conditionally and simultaneously specified spatial gaussian models – Markov random fields – Conditionally specified spatial models for discrete and continuous data – Parameter estimation for Lattice models using gaussian maximum likelihood estimation– Properties of estimators – Statistical image analysis and remote sensing.

Practical Assignments:

11.     Exercise on the estimation of parameters of lattice models

12.     Exercise on spatial autocorrelation

 

13.     Exercise on the fitting of lattice models 

Unit-5
Teaching Hours:15
Spatial point patterns
 

Spatial point patterns data analysis: Complete spatial randomness, regularity and clustering – Kernel estimators of intensity function – Distance methods: Nearest-Neighbor methods – Statistical spatial analysis of point processes:  Stationary and Isotropic point processes – Palm distribution – Models and model fitting: Inhomogeneous Poisson, Cox and Poisson cluster process

Practical Assignments:

14.     Exercise on plotting spatial point patterns under the boundary

15.     Exercise on distance methods

16.    Exercise on Kernel smoothing

 

17.     Exercise on Inhomogeneous Poisson process

Text Books And Reference Books:
  1. Cressie, Noel A.C. (2015). Statistics for Spatial Data. Revised Edition. Wiley Interscience Publication.
Essential Reading / Recommended Reading
  1. Bivand Roger S., Pebesma Edzer J.  and Gomez-Rubio V. (2013). Applied Spatial Data Analysis with R. Springer New York(2nd Edition).

 

Evaluation Pattern

CIA 50%+ESE 50%

MST572C - NON-PARAMETRIC INFERENCE (2022 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:4

Course Objectives/Course Description

 

This course will provide the basic theory and computing tools to perform nonparametric tests, including the Sign test, Wilcoxon signed-rank test, Median test etc. Kruskal-Wallis for one-way and multiple comparisons, linear rank test for location and scale parameters and measure of association in bivariate populations are other nonparametric tests covered in this course. The aim of the course is the in-depth presentation and analysis of the most common methods and techniques of non-parametric statistics such as sign test, rank test, run test, median test etc.

Course Outcome

CO1: Use statistical methods to construct and interpret interval estimators for population medians and other population parameters based on rank-based methods.

CO2: Compare different nonparametric hypothesis tests in two-sample problems.

CO3: Formulate, test and interpret various hypothesis tests for location, scale, and independence problems.

CO4: Demonstrate different measures of association for bivariate samples.

Unit-1
Teaching Hours:15
One-Sample and Paired-Sample Procedures
 

 

The quantile function - the empirical distribution function - statistical properties of order statistics- confidence interval for a population quantile -hypothesis testing for a population quantile -the sign test and confidence interval for the median - rank-order statistics -treatment of ties in rank tests-  Wilcoxon signed-rank test and confidence interval

 

PracticalAssignments:

  1. Exercise on confidence interval estimation and hypothesis test for a population Quantile
  2. Exercise on sign test and confidence interval for the median
  3. Exercise on rank-order statistics -treatment of ties in rank tests
  4. Exercise on Wilcoxon signed-rank test and confidence interval
Unit-2
Teaching Hours:15
The General two-sample problem
 

Wald-Wolfowitz runs test - Kolmogorov-Smirnov two-sample test - median test - the control median test - the Mann-Whitney U test                                                                                    

 

Practical Assignments:

 5.Exercise on Wald-Wolfowitz runs test

6.Exercise on Kolmogorov-Smirnov two-sample test.

7.Exercise on Median test and control median test.

 

8.Exercise on Mann-Whitney U test.

 

Unit-3
Teaching Hours:15
Linear Rank Tests for the Location and Scale Problem
 

Definition of linear rank statistics - Wilcoxon rank-sum test - mood test - Freund-Ansari-Bradley-David-Barton tests - Siegel-Tukey test

 

Practical Assignments:

9.Exercise on Wilcoxon rank-sum test and  mood test

10.Exercise on Freund-Ansari-Bradley-David-Barton tests.

11. Exercise on Siegel-Tukey test

 

Unit-4
Teaching Hours:15
Tests of the Equality of k Independent Samples
 

Extension of the median test - the extension of the control median test - the Kruskal-Wallis one-way ANOVA test and multiple comparisons - tests against ordered alternatives - comparisons with a control -  Chi-Square test for k proportions

 

Practical Assignments:

12.Exercise on the extension of the median test and control median test.

13.Exercise on Kruskal-Wallis one-way ANOVA test.

14.Exercise on chi-square test for k  proportions

 

Unit-5
Teaching Hours:15
Measures of Association for Bivariate Samples
 

Introduction: definition of measures of association in a bivariate population - Kendall’s Tau coefficient - Spearman’s coefficient of rank correlation - relations between R and T; E(R), t, and r 

 

Practical Assignments:

15.Exercise on Kendall’s Tau coefficient.

16.Exercise on Spearman’s coefficient of rank correlation

 

Text Books And Reference Books:
  1. Gibbons, J. D., & Chakraborti, S. (2020). Nonparametric statistical inference. CRC press.

  2. Kloke, J., & McKean, J. W. (2014). Nonparametric statistical methods using R. CRC Press.

 

Essential Reading / Recommended Reading
  1. Hollander, M., Wolfe, D. A., & Chicken, E. (2013). Nonparametric statistical methods (Vol. 751). John Wiley & Sons.
  2. Lewis, N. D. C. (2013). 100 Statistical Tests in R. Heather Hills Press.

 

Evaluation Pattern

CIA 50%

ESE 50%

MST581 - RESEARCH IMPLEMENTATION (2022 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:6
Max Marks:100
Credits:3

Course Objectives/Course Description

 

This will equip the student to apply statistical methods they have studied in various courses and present their work through research articles.

Course Outcome

CO1: Apply statistical methods in research articles.

Unit-1
Teaching Hours:75
Research Implementation
 

1. Apply various statistical methods in solving a real-life problem.

2. Comparison with the existing models or results.

3. Writing research article 

4. Presentation of the article

Text Books And Reference Books:

_

Essential Reading / Recommended Reading

-

Evaluation Pattern

CIA 50%

ESE 50%

MST681 - INDUSTRY PROJECT (2022 Batch)

Total Teaching Hours for Semester:0
No of Lecture Hours/Week:2
Max Marks:250
Credits:10

Course Objectives/Course Description

 

 This course helps the student to develop students to become globally competent and to inculcate Entrepreneurial skills among students.

Course Outcome

CO1: develop students to become globally competent.

CO2: Inculcate Entrepreneurial skills among students.

Unit-1
Teaching Hours:0
Project Work
 

It is a full time project to be taken up either in the industry or in an R&D organization

Text Books And Reference Books:

-

Essential Reading / Recommended Reading

-

Evaluation Pattern

CIA: 50%

ESE: 50%

MST682 - RESEARCH PUBLICATION (2022 Batch)

Total Teaching Hours for Semester:0
No of Lecture Hours/Week:0
Max Marks:50
Credits:2

Course Objectives/Course Description

 

This course has been conceptualized in order to equip the postgraduate students with the necessary skills for publishing their manuscripts in a Scopus/WoS indexed journal. 

Course Outcome

CO1: Publish research manuscripts.

Unit-1
Teaching Hours:0
Publication
 

Identification of journal - formatting the article - communicating the article - revision of the article

Text Books And Reference Books:

Mack, C. A. (2018). How to Write a Good Scientific Paper. United States: SPIE Press.

Essential Reading / Recommended Reading

Mack, C. A. (2018). How to Write a Good Scientific Paper. United States: SPIE Press.

Evaluation Pattern

CIA 50%+ESE 50%