MA 267: Introduction to Statistical Learning with Applications
Credits: 3:0
Exploratory Data Analysis and Descriptive Statistics, with basic introductory programming in R using tidyverse for data visualisation.
Sampling Distribution and Limit Theorems: Order Statistics, Chi^2, F, Student’s t. Sampling statistics from Normal Population, Law of Large numbers, Central Limit Theorem, Variance Stabilising transformation. Proofs via simulation in R.
Estimation: Method of Moments, Maximum Likelihood Estimate and Confidence intervals.
Hypothesis Testing: Binomial Test for proportion, Normal Test for mean when variance is known/unknown, two sample t-test for equality of means when variance is known.
Linear Models, Normal Equations, Gauss Markov Theorem, Testing of linear hypotheses. One-way and two-way classification models: ANOVA, Random effects. Emphasis on Numerical evaluation. Regularisation and Subset Selection methods.
Basics of Decision trees: Regression Tress, Classification trees and comparison with Linear Models.
Computational Optimal transport.
Applications from Epidemiology, Networks and Optimal transport.
Suggested books and references:
- Siva Athreya, Deepayan Sarkar and Steve Tanner, Probability and Statistics with Examples Using R, Institute of Mathematical Statistics, Hayward, CA.
- Sanford Weisberg, Applied Linear Regression, John Wiley and Sons, New York.
- Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, An Introduction to Statistical Learning, Springer-Verlag, New York.