CHRIST (Deemed to University), BangaloreDEPARTMENT OF STATISTICS_AND _DATA_SCIENCESchool of Sciences 

Syllabus for

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    5  4  100 
MST371  TIME SERIES ANALYSIS    8  5  150 
MST372  STATISTICAL MACHINE LEARNING    6  4  100 
MST373A  JAVA PROGRAMMING FOR DATA SCIENCE    5  3  100 
MST373B  CLINICAL TRIALS    5  3  100 
MST373C  RELIABILITY ENGINEERING    5  3  100 
MST381  RESEARCH  PROBLEM IDENTIFICATION AND FORMULATION    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  NONPARAMETRIC 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    2  10  250 
MST682  RESEARCH PUBLICATION    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 problemsolving skill through realtime 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 measuretheoretic and analytical techniques for understanding probability concepts. 

Course Outcome 

CO1: Relate measure and probability concepts. CO2: Analyze probability concepts using the measuretheoretic approach. CO3: Evaluate conditional distributions and conditional expectations. CO4: Make use of limit theorems in the convergence of random variables 
Unit1 
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.  
Unit2 
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).  
Unit3 
Teaching Hours:12 
Random Vectors


Random vectors – joint distribution function – joint moments  Conditional probabilities  Bayes’ theorem – conditional distributions – independence  Conditional expectation and its properties  
Unit4 
Teaching Hours:12 
Convergence


Modes of convergence: Convergence in probability, in distribution, in rth mean, almost sure convergence and their interrelationships  Convergence theorem for expectation  
Unit5 
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: LindbergLevy and Liaponov’s CLT.  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern
 
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 reallife phenomena. This course makes students understand different probability distributions and model reallife problems using them. 

Course Outcome 

CO1: Classify different families of probability distributions. CO2: Analyse wellknown 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. 
Unit1 
Teaching Hours:12 
Discrete Distributions


Modified power series family and properties  Binomial  Geometric Negative binomial, Logarithmic series  hypergeometric distribution and its properties.  
Unit2 
Teaching Hours:12 
Continuous Distributions


Pearsonian system of distributions  Beta, Gamma, Pareto and Normal as special cases of the Pearson family and their properties  
Unit3 
Teaching Hours:12 
Sampling distributions


Sampling distributions of the mean and variance from normal population  independence of mean and variance  chisquare, students t and F distribution and their noncentral forms  Order statistics and their distributions.  
Unit4 
Teaching Hours:12 
Multivariate distributions


Bivariate Poisson, Multinomial distribution  Multivariate normal (definition only)  bivariate exponential distribution of Gumbel  Marshall and Olkin distribution  Dirichlet distribution.  
Unit5 
Teaching Hours:12 
Distribution of Quadratic forms


Quadratic forms in normal variables: distribution and roperties  Cochran’ theorem: applications.  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern
 
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 
Unit1 
Teaching Hours:12 
System of linear equations


Matrix operations  Linear equations  row reduced and echelon form  Homogenous system of equations  Linear dependence  
Unit2 
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.  
Unit3 
Teaching Hours:12 
Linear transformations


Algebra of linear transformations  Matrix representations  rank nullity theorem  determinants  eigenvalues and eigenvectors  CayleyHamilton theorem  Jordan canonical forms  orthogonalisation process  orthonormal basis.  
Unit4 
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  
Unit5 
Teaching Hours:12 
Linear models


Fitting the model  ordinary least squares  estimability of parametric functions  GaussMarkov theorem  applications: regression model  analysis of variance.  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern
 
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 reallife problems. 
Unit1 
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  
Unit2 
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  
Unit3 
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  
Unit4 
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  
Unit5 
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. 
Unit1 
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.  
Unit2 
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 userdefined functions 5. Lab exercise on Recursive and Lambda function 6. Lab exercise on OOP Concepts  
Unit3 
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  
Unit4 
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  
Unit5 
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. 
Unit1 
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  
Unit2 
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, AddisonWesley.  
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 nonparametric tests. 

Course Outcome 

CO1: Apply the procedures of testing hypotheses for solving reallife 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 nonparametric tests and draw conclusions to reallife problems. 
Unit1 
Teaching Hours:12 
Generalized NeymanPearson Lemma and Onesided tests


Monotone Likelihood Ratio (MLR) property  Testing in oneparameter exponential families  Generalised NeymanPearson lemma (Statement only)  Unbiased and invariant tests  Locally most powerful tests  
Unit2 
Teaching Hours:12 
Uniformly most powerful tests


Onesided uniformly most powerful tests  Unbiased and Uniformly Most Powerful Unbiased tests for different twosided hypothesis  Extension of these results to Pitman family when only upper or lower end depends on the parameters  UMP test from αsimilar tests and αsimilar tests with Neyman structure.  
Unit3 
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  ttests  Ftests  
Unit4 
Teaching Hours:12 
Basics of nonparametric tests


Nonparametric tests: Sign test  Chisquare tests  KolmogorovSmirnov one sample and two samples tests  Median test  Wilcoxon Signed Rank test  Mann Whitney Utest  Test for Randomness  Runs up and runs down test  Wald–Wolfowitz run test for equality of distributions  Kruskal–Wallis oneway analysis of variance  Friedman’s twoway analysis of variance  Power and asymptotic relative efficiency.  
Unit5 
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. McMillan, 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). NonParametric 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. 
Unit1 
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.  
Unit2 
Teaching Hours:12 
Discrete time Markov chains


Markov Chains: Definition, Examples  Transition probability matrix  ChapmanKolmogorv 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.  
Unit3 
Teaching Hours:12 
Continuous time Markov chains and Poisson process


Transition probability function  Kolmogorov differential equations  Poisson process: homogenous process, interarrival time distribution, compound process  Birth and death process  Service applications: Queuing models Markovian models.  
Unit4 
Teaching Hours:12 
Branching process


GaltonWatson branching processes  Generating function  Extinction probabilities  Continuoustime branching processes  Extinction probabilities  Branching processes with general variable lifetime.  
Unit5 
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 nonlinear regression in reallife problems. CO4: Analyse the robustness of the regression model. 
Unit1 
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  
Unit2 
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.  
Unit3 
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 stepwise regression. 10. Selecting the best model using Forward and backward  
Unit4 
Teaching Hours:18 
Nonlinear regression


Nonlinear regression Introduction to general nonlinear regression  leastsquares in nonlinear case  estimating the parameters of a nonlinear system  reparameterization of the model  logistic regression Nonlinear growth models Practical Assignments: 11. Estimate parameters in nonlinear models using the least square procedure  
Unit5 
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 Mestimators. 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. 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. 
Unit1 
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.  
Unit2 
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  
Unit3 
Teaching Hours:15 

Introduction to Relational Database


 
Unit4 
Teaching Hours:15 

QUERY AND NORMALIZATION


 
Unit5 
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:
 
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 nonparametric methods of statistical data analysis. CO5: Demonstrate the concepts of Epidemiology 
Unit1 
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  
Unit2 
Teaching Hours:20 
Parametric and Non  Parametric methods


Parametric methods  one sample ttest  independent sample ttest  paired sample ttest  oneway analysis of variance  twoway analysis of variance  analysis of covariance  repeated measures of analysis of variance  Pearson correlation coefficient  Nonparametric methods: Chisquare test of independence and goodness of fit  Mann Whitney U test  Wilcoxon signedrank 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 nonparametric methods of analysis  
Unit3 
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  
Unit4 
Teaching Hours:15 
Epidemiology


Introduction to epidemiology, measures of epidemiology, observational study designs: case report, case series correlational studies, crosssectional studies, retrospective and prospective studies, analytical epidemiological studiescase 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 crosssectional study data 3. Exercise on analysis of casecontrol 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 ebook. 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 CIA50% 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 onedimensional 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. 
Unit1 
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.  
Unit2 
Teaching Hours:15 
Integer Linear Programming


Branch and bound algorithm – cutting plane algorithm – transportation problem: northwest method, leastcost 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.  
Unit3 
Teaching Hours:15 
Nonlinear Programming


Introduction – unimodal function – onedimensional 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  
Unit4 
Teaching Hours:15 
Classical optimization techniques


Single variable optimization – multivariable optimization with no constraints: semidefinite case and saddle point – multivariable optimization with equality constraints: direct substitution –method of constrained variation – method of Lagrange multipliers  KuhnTucker 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.  
Unit5 
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 CIA50% ESE50%  
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 nonparametric tests 

Course Outcome 

CO1: Apply the procedures of testing hypotheses for solving reallife 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 nonparametric tests and draw conclusions to reallife problems. 
Unit1 
Teaching Hours:12 
Generalized NeymanPearson Lemma and Onesided tests


Monotone Likelihood Ratio (MLR) property  Testing in oneparameter exponential families  Generalised NeymanPearson lemma (Statement only)  Unbiased and invariant tests  Locally most powerful tests  
Unit2 
Teaching Hours:12 
Uniformly most powerful tests


Onesided uniformly most powerful tests  Unbiased and Uniformly Most Powerful Unbiased tests for differenttwosided hypothesis  Extension of these results to Pitman family when only upper or lower end depends onthe parameters  UMP test from αsimilar tests and αsimilar tests with Neyman structure.  
Unit3 
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  ChiSquare tests  ttests  Ftests  
Unit4 
Teaching Hours:12 
Basics of nonparametric tests


Nonparametric tests: Sign test  Chisquare tests  KolmogorovSmirnov one sample and two samples tests Median test  Wilcoxon Signed Rank test  MannWhitney Utest  Test for Randomness  Runs up and runs down test  Wald–Wolfowitz run test for equality of distributions  Kruskal–Wallis oneway analysis of variance  Friedman’s twoway analysis of variance Power and asymptotic relative efficiency.  
Unit5 
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
2nd edition. McMillan, New York.
 
Evaluation Pattern CIA50%
ESE50%  
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, autocovariance 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. 
Unit1 
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 componentsElimination 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 leastsquare fitting to estimate and eliminate the trend component
 
Unit2 
Teaching Hours:18 
Stationary time series models


Stationary time series models  Concepts of weak and strongstationarity – General linear Process  AutoRegressive(AR),MovingAverage(MA)andAutoRegressiveMovingAverage(ARMA)processes – theirproperties conditionsforstationarity and invertibility model identification based onACF and PACF Maximum likelihood estimation – YuleWalkerEstimationorderselection(AICandBIC)Residual Analysis  Box Jenkins methodology to theidentificationofstationarytime
seriesmodels
PracticalAssignments:
5.ExerciseonfittingARmodel
6. ExerciseonfittingMAmodel
7. Exerciseonfitting ARMAmodel
8.Modelidentificationusing ACFandPACF,ModelselectionusingAIC andBIC
9.ResidualanalysisanddiagnosischeckforAR, MAandARMA models  
Unit3 
Teaching Hours:18 
Nonstationary time series models


Concept of nonstationarity  Spurious trends and regressions unit root tests : DickeyFuller (DF) test  Augmented Dickey Fuller(ADF) test – AutoRegressive 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 nonstationary series from various plots. 11.Exercise on testing nonstationarity using ADF test, Exercise on fitting ARIMA models. 12.Residual analysis and diagnosis check for ARIMA model.  
Unit4 
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  
Unit5 
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. 
Unit1 
Teaching Hours:15 
Statistical learning


Statistical learning: definitionprediction accuracy and model interpretabilitysupervised and unsupervised learningassessing model accuracy important problems in data mining: classification, regression, clustering, ranking, density estimation Concepts: training and testing, crossvalidation, 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  
Unit2 
Teaching Hours:15 
Classification algorithms


Logistic model training and testing the modellinear discriminant analysisquadratic discriminant analysis Use of Bayes’ theoremk 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 kNN classifiers 7. Lab exercise on Adaboost  
Unit3 
Teaching Hours:15 
Linear model selection and regularization


Optimal modelshrinkage methods: ridge and lasso regressionDimension reduction methods: principal component (PC) regression and partial least square (PLS) regression: Nonlinear models: regression splinespolynomial – 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  
Unit4 
Teaching Hours:15 
Treebased methods


Decision treeregression trees  bagging  random forests  boosting  classification treesboostingtree 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  
Unit5 
Teaching Hours:15 
Support vector machines and resampling procedures


Maximal classifiersupport vector classifierssupport  rank boost (ranking algorithm)  hierarchical Bayesian modelling for density  resampling techniquesbootstrap clustering algorithms: Kmeans 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 kmeans clustering  
Text Books And Reference Books:
 
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.".  
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 objectoriented structures. CO3: Design programs to handle files of different formats. CO4: Analyze data and visualize using appropriate libraries. 
Unit1 
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  
Unit2 
Teaching Hours:11 
Data structures in Java


Primitive data structure and Nonprimitive data structure  Array Processing  Multidimensional Arrays  String Methods  String Manipulation – Regular Expressions Practical Assignments: 3. Lab exercise on Arrays 4. Lab exercise on Strings  
Unit3 
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  
Unit4 
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 CollectionsInputOutput,Acessing DataCSV,JSON,DataFrames. Practical Assignments: 8. Lab exercise on handling CSV files 9. Lab exercise on handling JSON.  
Unit5 
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: McGrawHill 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. 
Unit1 
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  followup studies GCP/ICH guidelines  
Unit2 
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  nonrandomized concurrent controlled trials historical controls  cross over design  withdrawal design  hybrid designs – group allocation designs and studies of equivalency.  
Unit3 
Teaching Hours:12 

Methods of randomization


Fixed allocation randomization  stratified randomization  adaptive randomization  unequal randomization  Intervention and placebos  blinding in clinical trials: unblended trials  singleblind trials  double blind trials and tripleblind trials.  
Unit4 
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.  
Unit5 
Teaching Hours:12 

Data management


Design of case report form  data collection  intention to treat analysis and perprotocol 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 TrialsDesign, 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
 
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 stressstrength model for system reliability. 
Unit1 
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  
Unit2 
Teaching Hours:12 
Lifetime models


Nonmonotonic 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 upsidedown 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  
Unit3 
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  
Unit4 
Teaching Hours:12 
Reliability estimation


Reliability estimation using MLE: exponential, Weibull and gamma distributions based on censored and noncensored samples  UMVU estimation of reliability function  Bayesian reliability estimation of exponential and Weibull models Practical Assignments: 10. Exercise on ML estimation under noncensored samples. 11. Exercise on ML estimation under censored samples. 12. Exercise on Bayesian estimation of reliability.  
Unit5 
Teaching Hours:12 
Life testing


Life testing: basics – modelling lifetime – Accelerated Life Time (ALT) models cumulative exposure models (CEM)  exponential CEM – stressstrength reliability – exponential stressstrength model. Practical Assignments: 13. Exercise on basic life testing procedure. 14. Exercise on exponential CEM model. 15. Exercise on stressstrength 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 lifetesting models: theory and methods. Routledge.  
Essential Reading / Recommended Reading
 
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 reallife problem. CO2: Interpret and conclude the statistical analysis scientifically. CO3: Present the work done through presentation and research article. 
Unit1 
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 CIA100%
 
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 timetoevent 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 NonParametric Survival techniques for applications lifetime data CO4: Demonstrate the understanding of various Competing Risks and their effects 
Unit1 
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 nonparametric estimation in truncated and censored cases. Practical Assignments: 1.Lab exercise on the parametric estimation of left and rightcensored data 2.Lab exercise on the parametric estimation of truncated data 3.Lab exercise on the nonparametric estimation of censored and truncated data  
Unit2 
Teaching Hours:12 
Parametric Survival Models


Parametric forms and the distribution of log time  The exponential  Weibull  Gompertz  Gamma  Generalized Gamma  CoaleMcNeil  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
 
Unit3 
Teaching Hours:12 
NonParametric Survival Models


Onesample estimation with censored data  The KaplanMeier estimator  Greenwood's formula  The NelsonAalen estimator  The expectation of life  Comparison of several groups: Mantel Haenszel and the logrank test. Regression: Cox's model and partial likelihood  The score and information  The problem of ties  Tests of hypotheses  Timevarying covariates  Estimating the baseline survival  Martingale residuals. Practical Assignments: 7.Lab exercise on KaplanMeier estimator and NelsonAalen estimator 8.Lab exercise on Mantel Haenszel and the logrank test 9.Lab exercise on the Cox model with timevarying covariate  
Unit4 
Teaching Hours:12 
Models for Discrete Data and Extensions


Cox's discrete logistic model and logistic regression  Modelling grouped continuous data and the complementary loglog transformation  Piecewise 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 Piecewise regression for survival data  
Unit5 
Teaching Hours:12 
Models for Competing Risks


Modelling multiple causes of failure  Research questions of interest  Causespecific hazards  Overall survival  Causespecific densities  Estimation: onesample and the generalized Kaplan Meier and NelsonAalen estimators  The Incidence function  Regression models  Weibull regression  Cox regression and partial likelihood  Piecewise exponential survival and multinomial logits  The identification problem  Multivariate and marginal survival  The FineGray model. Practical Assignments: 13.Lab exercise on nonparametric 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 oneway and twoway 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. 
Unit1 
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.  
Unit2 
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 twoway classification with a single concomitant variable in CRD and RCBD designs.  
Unit3 
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.  
Unit4 
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.  
Unit5 
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 interblock 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
 
Evaluation Pattern
 
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 continuoustime Markov chains. CO4: Apply Brownian motion in finance problems.

Unit1 
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.  
Unit2 
Teaching Hours:12 

Discrete time Markov chains


Markov Chains: Definition, Examples  Transition probability matrix  ChapmanKolmogorv 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.  
Unit3 
Teaching Hours:12 

Continuous time Markov chains and Poisson process


Transition probability function  Kolmogorov differential equations  Poisson process: homogenous process, interarrival time distribution, compound process  Birth and death process  Service applications: Queuing models Markovian models.  
Unit4 
Teaching Hours:12 

Branching process


GaltonWatson branching processes  Generating function  Extinction probabilities  Continuoustime branching processes  Extinction probabilities  Branching processes with general variable lifetime.  
Unit5 
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
 
Evaluation Pattern
 
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 realtime applications. 
Unit1 
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.  
Unit2 
Teaching Hours:15 
Supervised Learning Algorithms


Concept of supervised learning algorithms  Perceptron networks  Adaptive linear neuron (Adaline)  Multiple adaptive linear neuron  BackPropagation network: Learning factors  Initial weights  Learning rate ɑ  Momentum factor  Generalization  Training and testing of the data.  
Unit3 
Teaching Hours:15 
Unsupervised Learning Algorithms


Concept of unsupervised learning algorithms  Fixed weight competitive net: Maxnet  Mexican Hat net  Hamming networks  Kohonen selforganizing feature maps  Learning vector quantization.  
Unit4 
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.  
Unit5 
Teaching Hours:15 
Deep Reinforcement Learning


Stateless algorithms: Naive algorithms  Upper bounding methods  Simple reinforcement learning for TicTacToe  StrawMan 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
 
Evaluation Pattern CIA50% ESE50%  
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. 
Unit1 
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.  
Unit2 
Teaching Hours:15 
Equilibrium law and SexLinked gene


Gene and genotypic frequencies  Random mating and HardyWeinberg 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.  
Unit3 
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.  
Unit4 
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.  
Unit5 
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 reallife data based on exploratory data analysis. CO5: Apply actuarial models to reallife data. 
Unit1 
Teaching Hours:15 
Introduction to actuarial statistics


Utility theoryintroduction  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  
Unit2 
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 KaplanMeier estimator  Nelson Aalen estimator  Cox proportional hazards and Kernel density estimators.
Practical Assignments: 3. Apply survival models to simple problems in longterm insurance, pensions and banking. 4. Preparation of life tables based on the real life data. 5. Estimation of survival distribution using KaplanMeier estimator, Nelson Aalen estimator, Cox proportional hazards and Kernel density estimators  
Unit3 
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.  
Unit4 
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  stoploss insurance.
Practical Assignments:
9. Illustrate discrete and continuous insurance benefits 10. Illustrate discrete and continuous annuity benefits  
Unit5 
Teaching Hours:15 
Data and Systems


Data as a resource for problemsolving  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:
 
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 reallife problem. CO3: Interpret and conclude the statistical analysis scientifically. CO4: Present the work done through presentation and research article. 
Unit1 
Teaching Hours:60 
Modelling


1. Apply various statistical methods in solving a reallife 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.

Unit1 
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. 
Unit1 
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.  
Unit2 
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 Vmask procedure – Tabular CUSUM charts  Construction of Moving range  movingaverage and geometric movingaverage control charts.  
Unit3 
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 MILSTD105D tables
 
Unit4 
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.  
Unit5 
Teaching Hours:12 
Continuous and Cumulative Sampling Plans


Continuous Sampling Plans (CSP): CSP1 CSP2  CSP3  SkipLot Sampling Plans (SkSP): SkSP1  SkSP2 with SSP as reference plan  Chain Sampling Plans (ChSP  1) with SSP as reference plan  TightenNormalTighted (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 McGrawHill, 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, IrwinIllinois, 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. 
Unit1 
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).  
Unit2 
Teaching Hours:12 
MANOVA and MANCOVA


Multivariate analysis of variance (MANOVA) and Covariance (MANCOVA) of one and twoway classified data with their interactions  Univariate and Multivariate TwoWay Fixedeffects Model with Interaction.  
Unit3 
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.  
Unit4 
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.  
Unit5 
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
CIA50% ESE50%  
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 
Unit1 
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, SemiStructured, Metadata  Big data sources: HumanHuman communication, HumanMachine Communication, MachineMachine Communication  Data Ownership  Data Privacy. Practical Assignments: 1. Setting up infrastructure and Automation environment 2. Case study for identifying Data Characteristics  
Unit2 
Teaching Hours:15 
Big Data Architecture


Standard Big data architecture  Big data application  Hadoop framework  HDFS Design goal  MasterSlave architecture  Block System  Readwrite 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
 
Unit3 
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  
Unit4 
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  
Unit5 
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 Builtin function  Userdefined functions  Pig Scripts. Practical Assignments: 14. Exercise on Hive Architecture 15. Exercise on Pig Architecture
 
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
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 
Unit1 
Teaching Hours:15 
Introduction


Definition and scope of demography Importance of demographic analysis  Sources of demographic data  census, registration, adhoc surveys  Hospital records  Demographic profiles of the Indian Census Practical Assignments:
 
Unit2 
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
 
Unit3 
Teaching Hours:15 
Measurement of Fertility


Crude birth rate  General fertility rate  Agespecific birth rate  Total fertility rate  Gross reproduction rate  Net reproduction rate.  
Unit4 
Teaching Hours:15 
Measurement of Mortality


Crude death rate  Standardized death rates  Agespecific death rates  Infant Mortality rate  Death rate by cause. Practical Assignments:
 
Unit5 
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:
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
 
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 doseresponse models. CO4: Apply risk management to individual portfolio problems 
Unit1 
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  
Unit2 
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  
Unit3 
Teaching Hours:15 
Advanced Statistical Risk Modelling


Statistical DoseResponse 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 DoseResponse 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  
Unit4 
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
 
Unit5 
Teaching Hours:13 
Individual Risk Management Decisions


Value Functions and Risk Profiles  Rational Individual RiskManagement via Expected Utility  EU DecisionModeling Basics  DecisionMaking 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 decisionmaking algorithms  
Text Books And Reference Books:
 
Essential Reading / Recommended Reading
 
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. 
Unit1 
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:
 
Unit2 
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:
 
Unit3 
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 OneSided Hypothesis  Testing a TwoSided Hypothesis. Bayesian Inference for Poisson: Some Prior Distributions for Poisson  Inference for Poisson Parameter. Practical Assignments:
 
Unit4 
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:
 
Unit5 
Teaching Hours:15 
Bayesian Computations


Analytic approximation  EM Algorithm  Monte Carlo sampling  Markov Chain Monte Carlo Methods  MetropolisHastings Algorithm  Gibbs sampling: examples and convergence issues. Practical Assignments:
 
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
 
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. 
Unit1 
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, SquareRootDifferences 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  
Unit2 
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 variogramparameter estimators, Crossvalidating 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  
Unit3 
Teaching Hours:15 
Spatial prediction and kriging


Scale of variation  Ordinary Kriging: Effect of variogram parameters on Kriging, Lognormal and TransGaussian Kriging, Cokriging – Robust Kriging – Universal Kriging : Estimation of variogram for Universal Kriging – MedianPolish Kriging: Gridded and nongridded data, Median Polishing spatial data, Bias in MedianBased covariogram estimators – Applications of Geostatistics. Practical Assignments: 8. Exercise on Ordinary Kriging 9. Exercise on Robust Kriging
10. Exercise on Universal Kriging  
Unit4 
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  
Unit5 
Teaching Hours:15 
Spatial point patterns


Spatial point patterns data analysis: Complete spatial randomness, regularity and clustering – Kernel estimators of intensity function – Distance methods: NearestNeighbor 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:
 
Essential Reading / Recommended Reading
 
Evaluation Pattern CIA 50%+ESE 50%  
MST572C  NONPARAMETRIC 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 signedrank test, Median test etc. KruskalWallis for oneway 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 indepth presentation and analysis of the most common methods and techniques of nonparametric 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 rankbased methods. CO2: Compare different nonparametric hypothesis tests in twosample problems. CO3: Formulate, test and interpret various hypothesis tests for location, scale, and independence problems. CO4: Demonstrate different measures of association for bivariate samples. 
Unit1 
Teaching Hours:15 
OneSample and PairedSample 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  rankorder statistics treatment of ties in rank tests Wilcoxon signedrank test and confidence interval
PracticalAssignments:
 
Unit2 
Teaching Hours:15 
The General twosample problem


WaldWolfowitz runs test  KolmogorovSmirnov twosample test  median test  the control median test  the MannWhitney U test
Practical Assignments: 5.Exercise on WaldWolfowitz runs test 6.Exercise on KolmogorovSmirnov twosample test. 7.Exercise on Median test and control median test.
8.Exercise on MannWhitney U test.
 
Unit3 
Teaching Hours:15 
Linear Rank Tests for the Location and Scale Problem


Definition of linear rank statistics  Wilcoxon ranksum test  mood test  FreundAnsariBradleyDavidBarton tests  SiegelTukey test
Practical Assignments: 9.Exercise on Wilcoxon ranksum test and mood test 10.Exercise on FreundAnsariBradleyDavidBarton tests. 11. Exercise on SiegelTukey test
 
Unit4 
Teaching Hours:15 
Tests of the Equality of k Independent Samples


Extension of the median test  the extension of the control median test  the KruskalWallis oneway ANOVA test and multiple comparisons  tests against ordered alternatives  comparisons with a control  ChiSquare test for k proportions
Practical Assignments: 12.Exercise on the extension of the median test and control median test. 13.Exercise on KruskalWallis oneway ANOVA test. 14.Exercise on chisquare test for k proportions
 
Unit5 
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:
 
Essential Reading / Recommended Reading
 
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. 
Unit1 
Teaching Hours:75 
Research Implementation


1. Apply various statistical methods in solving a reallife 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. 
Unit1 
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. 
Unit1 
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% 