Graduate Program

Course Credit: 3

Introduction Bayesian statistics refers to practical inferential methods that use probability models for both observable and unobservable quantities. 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. Objectives Acquire basic understanding in the principles and techniques of Bayesian data analysis. Ap- ply Bayesian methodology to solve real-life problems. Utilize R for Bayesian computation, visualization, and analysis of data. Learning Outcomes Upon completion of the course, students will learn about (i) the concept of the Bayesian statistical methods, (ii) formulation and derivation of prior and posterior distributions, (iii) estimation of the model using di erent MCMC methods, and (iv) application of the Bayesian methods to analyze data and interpret and compare results with the frequentist approach.

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

Introduction Spatial statistics encompasses diversi ed statistical methods for analyzing data obtained from stochastic process indexed by the space. This branch is enrich enough to gain insight from data exploiting the dependence over space. Its myriad applications caught profound attention of people from both academia and practitioners. 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. Learning Outcomes After completing this course students are expected to have knowledge about (i) spatial and non spatial data, (ii) geostatistical data and analysis, (iii) spatial interpolation, (iv) apply auto regressive model to areal data, (v) point pattern data analysis

Course Credit: 3

Introduction The course provides an introduction to causal inference with a cohesive presentation of con- cepts of, and methods for, causal inference. 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. Learning Outcomes Upon completion of the course, students are expected (i) to be familiar with the concepts of causality and counterfactuals (ii) to learn di erent methods for estimating causual e ects in the context of biomedical research (iii) to apply the methods to data obtained from observa- tional studies and to interpret the results.

Course Credit: 3

Analysis of Longitudinal Data Credit 3 Introduction Longitudinal data arise when multiple measurements of a response are collected over time for each individual in the study and hence are likely to be correlated, which presents substantial challenge in analyzing such data. This course covers topics related to statistical methods and models for drawing scienti c inferences from longitudinal data. Objectives The objectives of the course are to teach students to understand the unique features of and the methodological implication of analyzing the data from longitudinal studies, as compared to the data from traditional studies, to understand statistical methods/models, particularly linear/generalized linear mixed models, GEE approaches for analyzing longitudinal data. It is also expected that students will be familiar with the proper implementation and interpreta- tion of the statistical methods/models for analyzing longitudinal data and software packages analyzing such data. Learning Outcomes Upon completion of the course, students will achieve skills (i) to understand the nature of longitudinal/clustered data (ii) to understand the models and methods for analysing longitu- dinal/clustered data (iii) to analyse such data and interpret the results and (iv) to understand and interpret research ndings of the published reports and articles.

Course Credit: 3

Introduction Much of the information around us can be described as signals. Statistical signal process- ing uses stochastic processes, statistical inference and mathematical techniques to describe, transform, and analyze signals in order to extract information from them. Objectives This course is designed to provide statistics graduate students with 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. Its objective is to introduce students to real life applications demonstrating the use of statistics in signal analysis. Learning Outcomes At the end of this course a student should be able to : (i) understand basic concepts of signals, signal properties and their representations in time and frequency domains (ii) Apply well-known statistical estimation techniques to estimate signal parameters from noisy signal measurements (iii) Apply well-known statistical decision theory methods to detect signals in Gaussian noise and assess the performance of these methods (iv) Understand and appreciate the importance of statistics in solving real life problems occurring in the domain of signal processing and communication.

Course Credit: 3

Introduction Meta-analysis refers to the quantitative analysis of study outcomes. Meta-analysis consists of a collection of techniques that attempt to analyze and integrate results that accrue from research studies. This course provides an overview of systematic review and meta-analysis from a statistician's point of view. Objectives The main objectives are to introduce students with the merits of meta-analysis and how it can form an important and informative part of a systematic review, with the most common statistical methods for conducting a meta-analysis, and with how to analyze and interpret the results. Learning Outcomes At the end of the course, students should be familiar with (i) the research synthesis, (ii) systematic review of the existing research (iii) data extraction from systematic review, and (iv) models and methods for analyzing meta-data for new ndings and publication.

Course Credit: 3

Introduction The clinical trial is \the most de nitive tool for evaluation of the applicability of clinical research". It represents \a key research activity with the potential to improve the quality of health care and control costs through careful comparison of alternative treatments". The course is designed to give an overall idea of clinical trial studies. It will provide an introduction to the statistical and ethical aspects of clinical trials research. Objectives The main objectve o fthe course is to teach students on the topics include design, implemen- tation, and analysis of trials, including rst-in- human studies, phase II and phase III studies. The course will enable applying existing methodologies in designing clinical trials and will also foster research in this area. Learning Outcomes Upon completion of the course, students will achieve skills (i) to understand, design a trial for assess the e ectiveness of a drug, and (ii) to implement and analysis data from such trials and interpret the results.

Course Credit: 3

Introduction The course provides a broad but thorough introduction to the methods and practice of sta- tistical machine learning and its core models and algorithms. Objectives The aim of the course is to provide students of statistics with detailed knowledge of how Ma- chine Learning methods work and how statistical models can be brought to bear in computer systems not only to analyze large data sets, but also to let computers perform tasks, that traditional methods of computer science are unable to address. Learning Outcomes After completing the course, students will have the knowledge and skills to: i) Describe a num- ber of models for supervised, unsupervised, and reinforcement machine learning, ii) Assess the strength and weakness of each of these models, iii) Know the underlying mathematical rela- tionships within and across statistical learning algorithms, iv) Identify appropriate statistical tools for a data analysis problems in the real world based on reasoned arguments, v) Develop and implement optimisation methods for training of statistical models, vi) Design decision and optimal control problems to improve performance of statistical learning algorithms, vii) Design and implement various statistical machine learning algorithms in real-world applica- tions, viii) Evaluate the performance of various statistical machine learning algorithms, ix) Demonstrate a working knowledge of dimension reduction techniques. Identify and implement advanced computational methods in machine learning.

Course Credit: 3

Introduction 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 and computer programming. 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. Learning Outcomes The principal aim of this course is to (i) introduce Big Data and its characteristics and challenges to students, (ii) teach them appropriate tools for managing and analyzing such large-scale data, (iii) help students underst

Course Credit: 3

Introduction The course is typically designed for students who have a basic understanding of mathematics, programming, and machine learning concepts. The course provides a broad but thorough introduction to the methods and practice of advanced statistical machine learning and its core methods, models, and algorithms. 24 Objectives The aim of the course is to provide students of Applied Statistics and Data Science with de- tailed knowledge of how advanced Machine Learning methods work and how statistical mod- els can be brought to bear in computer systems not only to analyze large, high-dimensional, unstructured, and big data sets but also to let computers perform tasks e ciently, that tra- ditional methods of statistical and computer science are unable to address. Students will understand the underlying theory and perform assignments that involve a variety of real- world datasets from a variety of domains. They will learn recent statistical techniques based on a synthesis of resampling techniques, and neural networks that have achieved remarkable progress and led to a great deal of commercial and academic interest. Learning Outcomes After successful completion of the course, students are expected to (i) Describe a number of advanced machine learning techniques including deep learning, neural network and rein- forcement machine learning, (ii) Assess the strength and weaknesses of each of these models, (iii) Know the underlying mathematical relationships within and across statistical learning algorithms, iv) Identify appropriate statistical tools for a data analysis problems in the real world based on reasoned arguments, v) Develop and implement optimisation algorithms for advanced models, (vi) Design decision and optimal control problems to improve performance of statistical learning algorithms, (vii) Design and implement various advanced statistical ma- chine learning algorithms in real-world applications, (viii) Have an understanding of how to choose a model to describe a particular type of data, ix) Evaluate the performance of various advanced statistical machine learning algorithms.

Course Credit: 2

Introduction 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. Objectives This course aims to give the students a working knowledge of Python programming. Students will learn programming fundamentals, basic data structures, writing functions, importing and exporting data of di erent formats, data manipulation, and data visualization using Python. This course will also prepare students for more advanced courses in data science and machine learning. Learning Outcomes At the end of this course, students are expected to (i) understand the fundamentals of Python programming, (ii) produce insights from data through exploratory data analysis, and (iii) create e ective data visualizations using Python.

Course Credit: 2

Introduction This course focuses on the application of Bayesian statistics, geostatistical and spatio-temporal models in real-life situations. Objectives The successful completion of the course will help a student to apply methods related to Bayesian statistics and environmental statistical models in various domains. Learning Outcomes After completing the course, students will be familiar with (i) handling any computation re- lated to Bayesian models (ii) several Bayesian models including prior and posterior distribu- tions, Bayesian linear regression, MCMC techniques|Gibbs, Metropolis-Hastings, and their implementations, (iii) Bayesian test of hypothesis (iv) geostatistical data and their methods and models (v) Spatio-temporal models and Bayesian approach of spatio-temporal models.

Course Credit: 2

Introduction The course focuses on applications related to longitudinal data and causal inference. 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. Learning Outcomes At the end of the course students will achieve skills on (i) how to use statistical software and packages to analyse longitudinal/cluster/spatial data (ii) to t models and interpret the results (iii) to compare and identify the appropriate models required for the data (iv) to analyse data for estimating di erent causal estimands using observational data, and (v) to write report with statistical results for scienti c publications.

Course Credit: 2

Introduction The course focuses on applications related to machine learning, big data analytics, and sta- tistical signal processing. Objectives The successful completion of the course will help a student to apply methods related to advanced statistical machine learning, Big data analytics, and statistical signal processing in various domains. Learning Outcomes After completing the course, students will be familiar with (i) handling any computation related to big data analytics and advanced statistical Machine Learning techniques using R or Python software (ii) with di erent machine learning techniques including classi cation trees, CART, regularized regression models for high-dimensional data, spline, gam, ensembled methods-bagging, boosting, random forest, and SVM, (iii) implementation of skills of machine learning tools to any raw datasets, and (iv) sampling signals, signal quantization, noise removal using Fourier transform, estimation of signal parameters.

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

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. AST551:

Course Credit: 6

After three months of the start, each student of Group B will submit and present a short thesis proposal (length 3-5 A4 pages excluding references, 1.5 line spacing). The proposal will be evaluated by the internal members of the examination committee. Written evaluation on the proposal will be provided to the students explaining the possible improvement and in case of \Not satisfactory" proposals, the reasons for \Not satisfactory" performance will be stated in the written evaluation. In case of \Not satisfactory" performance the examination committee may give the student a second opportunity for proposal presentation. Students with \Not-Satisfactory" performance will be transferred to the Group A. The nal submission of the thesis will be required within 4 months of the completion of nal exam. Thesis will be examined by two external (outside the institute) examiners. Should it be required, the examination committee may consider one internal and one external examiner. Submitted thesis has to be defended at a presentation evaluated by the members of the examination committee. Forty percent (40%) weight will be allotted for thesis defense and remaining 60% weight for thesis itself.