Calendar

(Week 1) Recap of Probability Theory

Jan 8

Random Variables, Distributions, Expectation, Variance, Inverse CDF, Moment Generating Functions (MGF)

Rice, Chapter 2 and 4

(Week 2) Recap of Probability Theory

Jan 13

MGF continued, Joint and Conditional Distribution, Conditional Expectation, Chisquared R.V. Change of variable formula

Rice, Chapter 3 (3.5, 3.6) and Chapter 4 (4.4).

Jan 14

Practice Problem 1 released on Canvas

Jan 15

Variance, Covariance, Correlation, the multivariate Gaussian distribution

Rice 6.2 (review Rice 3.2-3.3, 4.3 if necessary)

(Week 3) Asymptotics and Introduction to Estimation

Jan 20

Asymptotics and Simulations

Rice, Chapter 5.1-5.3

Lab 1 on simulation of LLN and CLT

Solution to Practice Problems 1 posted on canvas

Jan 22

Introduction to Estimation

Rice 8.1.

Quiz 1 in class.

(Week 4) Parametric Estimation

Jan 27

Introduction to parameter estimation, fitting distributions, method of moments, examples, intro to MLEs.

Rice 8.1 - 8.5

Practice Problems 2 posted on canvas

Jan 29

Examples of the method of moments. Maximum Likelihood Estimates (MLE)

Rice 8.5

(Week 5) Parametric Estimation

Feb 1

Practice Problems 3 on MLEs posted on Canvas.

Feb 3

Desirable properties of estimators: unbiasedness, consistency. The concept of UMVUE, Fisher Information, and Cramer-Rao Lower Bound (CRLB)

Rice 8.7, 8.5.2

Feb 5

Lab 2 on parametric estimation

Quiz 2 in class

(Week 6) Bayesian

Feb 9

Coding assignment 1 posted on Canvas.

Feb 10

Proof of CRLB, Asymptotic Properties of MLE and other estimates, and confidence intervals

Rice 8.5.2 - 8.5.3

Feb 12

The the delta method, Introduction to Bayesian Inference

Rice 8.6

(Week 7) Estimation

Feb 17

Sufficiency, factorization theorem and examples

Rice 8.8

Feb 19

Rao-Blackwell theorem to find UMVUEs and examples

Rice 8.8

Feb 19

Quiz 3 in class

(Week 8) Midterm 1

Feb 24

Midterm Review.

Feb 26

Midterm 1

In class, 2:30pm - 4:00pm