Graduate Program

Course Credit: 3

Course Description This course describes Bayesian methods, in which the knowledge about the parameters or hypotheses continually modi ed as new data becomes available. The exibility and generality of these methods allow them to address complex real-life problems that are not amenable to other techniques. This course will provide a pragmatic introduction to Bayesian data analysis and its powerful applications. Course Objectives The objectives of the course are to acquire basic understanding in the principles and techniques of Bayesian data analysis and apply the Bayesian methodologies for Bayesian computation, visualization, and analysis of data to solve real-life problems.

Course Credit: 3

Introduction An introduction to methods of analysing correlated time-to-event data is provided in this course. Some commonly used methods for analysing univariate time-to-event data, e.g. Kaplan-Meier estimate of survivor functions, Cox's proportional hazards models, etc., are reviewed using counting processes notations. Objectives The objectives of the course are to teach the theoretical basis of di erent methods related to analysing correlated time-to-event data and competing risks model and to apply statistical softwares to analyse data using such models. Learning Outcomes At the end of the course, students are expected (i) to understand the theoretical basis of di erent methods related to analysing correlated time-to-event data and competing risks model (ii) to use a statistical software (e.g. related R packages) to analyse data using such models (iii) to interpret the results and write scienti c publication.

Course Credit: 3

Course Description The main objectives of this course is to acquaint students with the methodologies associated with the advanced sampling techniques. This course introduces advanced sampling methods used in sample survey. It covers sampling of unequal clusters, two-stage sampling, multistage sampling, methods for estimating variance in complex surveys, and non-sampling errors. 17 Course Objectives Technology is indispensable for modern life, and its advances in di erent aspects of our life made several things possible. Now a days data have been collected along with extensive additional information. Spatial data is one of such examples. In recent years, analysis of spatial data receives great attention over the world. As a result, several theories have been developed for di erent types of spatial data analysis. This course is designed to introduce the graduate student with few of such theories so that they can develop their skill in spatial data analysis. To comprehend this course, students need a sound knowledge of Mathematical statistics, particularly the concepts of stochastic process. It is expected that the student will be able to analyze di erent spatial data from diverse elds after successful completion of the course.

Course Credit: 3

Course Description The course provides an introduction to causal inference with a cohesive presentation of con- cepts of, and methods for, causal inference. Couse Objectives The aim of the course is to facilitate students to de ne causation in biomedical research, describe methods to make causal inferences in epidemiology and health services research, and demonstrate the practical application of these methods.

Course Credit: 3

Course Description Longitudinal and clustered data arise in diverse areas of research which presents substantial challenge in analyzing such data. This course covers topics related to statistical methods and models, such as population average model and mixed e ect models, for drawing scienti c inferences from longitudinal and clustered data. This course also covers topic related to methods for anayzing misisng data. Course Objectives The objectives of the course are to make students familiar with the unique features of and the methodological implication of analyzing the longitudinal and clustered data and to develop skills to formulate and estimate models for analyzing such data and interpret the ndings to di erent stakeholders.

Course Credit: 3

Much of the information around us can be described as signals. Statistical signal processing uses stochastic processes, statistical inference and mathematical techniques to describe, trans- form, and analyze signals in order to extract information from them. This course introduces basic concepts in signal processing and familiarizes students with the statistical methods used to solve real life problems in the eld. Course Objectives The objective of this course is to provide graduate students in statistics an overview of di erent types of signals, their representations and the use of statistical methods, such as estimation and hypothesis testing, to extract information from signals. It introduces students to real life applications of statistics in signal processing thus motivating research in this eld.

Course Credit: 3

Course Credit: 3

Course Credit: 3

Course Description The course provides a broad but thorough introduction to the methods and practice of basic statistical machine learning and its core methods, models, and algorithms. This course is about providing students of applied statistics and data science with detailed knowledge of how the basic Machine Learning methods work and how statistical models can be brought to bear in computer systems not only to analyze large, high-dimensional, and big data sets but also to let computers perform tasks, that traditional methods of computer science are unable to address. Course Objectives After completing the course students will be familiar with the concept of Arti cial Intelligence, Big Data, and their areas. describe several models for supervised and unsupervised machine learning and regularized modeling techniques, assess the strengths and weaknesses of each of these models, know the underlying mathematical relationships within and across statistical learning algorithms, develop and implement optimization methods for training of statistical models, design decision and optimal control problems to improve the performance of statistical learning algorithms, design and implement various statistical machine learning algorithms in real-world applications, evaluate the performance of various statistical machine learning 24 algorithms, demonstrate a working knowledge of dimension reduction techniques. identify and implement advanced computational methods in machine learning.

Course Credit: 3

Course Description This course is designed to introduce key computational concepts, tools and techniques for cu- rating, managing, and analyzing data of large volume, various types and di erent frequencies. This course assumes basic exposure to the concepts of arti cial intelligence, machine learning algorithms, deep learning and computer programming. Course Objectives The principal aim of this course is to introduce Big Data and its characteristics and challenges to students, and to teach them appropriate tools for managing and analyzing such large-scale data. Further objectives include helping students understand applications of Big Data in di erent elds and also ethical issues related to Big Data.

Course Credit: 3

Course Credit: 2

Course Description Python has become one of the most popular programming languages for data science due to its simplicity, versatility, and robust data analysis and machine learning capabilities. As organizations continue to digitize and generate increasingly large amounts of data, open- source tools like Python can enable data manipulation and exploration, machine learning, and statistical analysis in a scalable manner. This course provides a gentle introduction to programming in Python and its applications in data science and analytics. Course Objectives To give students a working knowledge of Python programming. To teach programming fun- damentals, basic data structures, writing functions, and importing and exporting data in di erent formats. To cover data manipulation and data visualization using Python. To pre- pare students for more advanced courses in data science and machine learning.

Course Credit: 2

Course Description This course focuses on the application of Bayesian statistics, geostatistical, and spatio-temporal models in real-life situations. This course covers hands-on training on statistical software for Bayesian computations, tting spatio-temporal models, and interpreting the results. Course Objectives The objectives of the courses are to make students familiar with the application of the meth- ods related to Bayesian statistics and geo-statistical models to data from diverse areas, pro- vide hands-on training on statistical software for Bayesian computations, and tting spatio- temporal models and interpret the results among di erent stakeholders.

Course Credit: 2

The course focuses on applications related to longitudinal data and causal inference. Course Objectives The course intends to train students with modern tools of analysing longitudinal data and making causal conclusion from real life data and small area estimation techniques.

Course Credit: 2

Course Description The course focuses on applications related to machine learning, big data analytics, and sta- tistical signal processing in various domains. Course Objectives After completing the course, students will be familiar with handling any computation related to big data analytics and advanced statistical Machine Learning techniques using R or Python software; with di erent machine learning and deep learning techniques including classi cation trees, CART, regularized regression models for high-dimensional data, spline, gam, ensembled methods-bagging, boosting, random forest, SVM, neural network; implementation of skills of machine learning tools to any raw datasets. In addition, students will learn to use MATLAB or Python for performing signal sampling, quantization, denoising of signals, estimation of parameters from noisy signals, etc.

Course Credit: 2

Each student (Group A and Group B) must be examined orally by a committee of selected members at the end of the academic year.

Course Credit: 3

Assessment of the non-credit seminar course will be either \Satisfactory" or \Non-satisfactory". To get a "Satisfactory" grade, each student needs to attend at least 70% of the seminars or- ganised by the institute during the academic year.

Course Credit: 6

Each student should be either in the project report group or in the internship group that the student will decide after discussing with the respective assigned supervisor. Students must submit their project report or internship report within two months of completing the nal examination. The internal members of the examination committee will evaluate the performance of the students in the seminars and the project report or internship report will be evaluated by two examiners nominated by the examination committee. The supervisor cannot evaluate the project or internship report that s/he has supervised. For this course, 50% weight of the course will be allotted to report, 10% weight for supervisor, and the remaining 40% weight will be for a seminar presentation.