Applications Open now for September 2024 Batch | Applications Close: Sep 15, 2024 | Exam: Oct 27, 2024

Applications Open now for September 2024 Batch | Applications Close: Sep 15, 2024 | Exam: Oct 27, 2024

Degree Level Course

Statistical Computing

To introduce computational methods involved in statistical estimation and learning problems.

by Dootika Vats

Course ID: BSMA3014

Course Credits: 4

Course Type: Elective

Pre-requisites: None

Course structure & Assessments

12 weeks of coursework, weekly online assignments, 2 in-person invigilated quizzes, 1 in-person invigilated end term exam. For details of standard course structure and assessments, visit Academics page.

WEEK 1 Introduction to R, Introduction to Monte Carlo, Pseudorandom Number Generation, Sampling Discrete Random Variables: Inverse Transform Method
WEEK 2 Discrete: Accept-Reject Algorithm, Composition Method, Sampling Continuous Random Variables: Inverse Transform Method
WEEK 3 Continuous: Accept-reject Algorithm with examples, Box-Muller method
WEEK 4 Continuous: Ratio-of-Uniforms method, examples and code, miscellaneous methods in sampling, Sampling from multivariate distritbutions
WEEK 5 Simple Importance Sampling: Examples, bias, variance, consistency, Optimal proposals,
WEEK 6 Weighted importance sampling: Examples, Review of likelihood functions, MLE examples
WEEK 7 Linear regression as MLE, Penalized regression, No-closed form MLEs, Review of Taylor Series Approximations
WEEK 8 Newton's optimization algorithm: examples and code, Gradient Descent algorithm, applications to logistic regression with code
WEEK 9 MM algorithm, application to Bridge Regression, EM algorithm, Introduction to Gaussian Mixture Model
WEEK 10 EM algorithm for GMM, Cross-validation with examples
WEEK 11 Bootstrapping: examples and code. Application to bridge regression, stochastic gradient descent
WEEK 12 Applications of SGD with code. Simulated annealing: examples, codes, and challenges
+ Show all weeks

Prescribed Books

The following are the suggested books for the course:

“Simulation” by Sheldon Ross, Elsevier, Fifth Edition

“Monte Carlo Statistical Methods” by Christian Robert and George Casella, Springer, 2004.

About the Instructors

Dootika Vats
Assistant Professor, Department of Mathematics and Statistics, IIT Kanpur

Dootika Vats is an Assistant Professor in the Department of Mathematics and Statistics at the Indian Institute of Technology, Kanpur. Previously, she was an NSF Postdocotoral fellow with Prof. Gareth Roberts at the University of Warwick. Her PhD was from the University of Minnesota, Twin-Cities working with Prof. Galin Jones.