STAT 200B: Statistical Theory

This is a graduate course on the theory of statitical inference and learning.

(1) Modes of statistical inference: point estimate, hypothesis testing, confidence interval, likelihood, sufficiency, Bayesian inference, decision theory, Stein estimator. (running examples: inference of binomial probability and normal means)
(2) Linear regression: best linear unbiased estimator, model complexity, training error and testing error, bias and variance, L2 and L1 regularization.
(3) Maximum likelihood: asymptotic optimality among estimating equations, Fisher information, Cramer-Rao bound, EM, likelihood ratio test, Akaike information criterion. (running examples: logistic regression, exponential family model, mixture model, latent variables and missing data, goodness of fit test, test of independence)
(4) Machine learning: PAC learning, VC dimension, perceptron, SVM, adaboost, unsupervised learning. (presented from a statistician's perspective)