Introduction

Time and location: We meet at 7:00 pm - 8:20 pm in GHC 4307 on Mar 21, Mar 28, Apr 4, Apr 11, Apr 18, Apr 25 (6 lectures). Course materials: a handout and a lecture note on Canvas Homeworks:

• on Canvas

• submit on Gradescope

• due every Friday at 1 pm with no extension

• lowest homework grade is dropped

• solutions outside of Weina's office GHC 9231

Office hours: 259 office hours of Weina, Tianxin, and Alec

Grading:

• Weekly homework (~2 problems/homework) -- 60% (drop lowest)

• Three quizzes -- 40% (drop lowest)

Syllabus

Statistical Estimation and Inference

Lecture 1: Basics of statistics: data generating models, common problem formulations and goals – Point estimation of parameters

• Likelihood function, log likelihood

• Maximum likelihood estimator (MLE)

Lecture 2: Bayesian estimation

• Priors

• Bayes update, maximum a posteriori (MAP) estimator

• Error metrics, minimum mean square error (MMSE) estimator

Lecture 3: Hypothesis testing

• Hypotheses, samples

• Type I and type II errors

• ML decision rule, MAP decision rule ∗ Minimum cost testing

Lecture 4: Confidence interval

• Point estimation vs interval estimation

• Sampling theory

• Connection with hypothesis testing

Prediction

Lecture 5: Classification

• Problem formulation, classifiers

• Error rate, empirical/training error

• Bayes classifier, regression functions

• Plug-in classifier

• Classifiers used in practice

Lecture 6: Regression

• Linear regression, least squared error

• Linear regression of a random variable on a random variable

• Least squared error (LSE) estimator

• Linear regression with Gaussian noise