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 |
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 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.
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