Calendar

(Week 1) Recap of Probability Theory

Aug 25
Random Variables, Distributions, Expectation, Variance, Inverse CDF, Moment Generating Functions (MGF)
Chapter 2 and 4
Aug 27
MGF continued, Joint and Conditional Distribution, Conditional Expectation, Chisquared R.V. Change of variable formula
Chapter 3 (3.5, 3.6) and Chapter 4 (4.4).
Aug 29
HW 1 released on Canvas
Due on Sep 12.

(Week 2) Sample Surveys

Sep 1
No Class due to Labor Day
Sep 3
Introduction to sample surveys, Sampling bias, Simple random sampling with replacement vs. without replacement, properties of sample mean
Chapter 7.1 - 7.3.1

(Week 3) Sample Surveys

Sep 8
Variance of sample mean for sampling with and without replacement, estimation of the population variance
Chapter 7.3.1 - 7.3.2
Sep 10
Central Limit Theorem, Asymptotic properties of sample mean, confidence intervals
Chapter 7.3.3
Sep 12
HW 1 is due on Gradescope
HW 2 released on Canvas
Due on Sep 26.

(Week 4) Parametric Estimation

Sep 15
Confidence intervals continued. Introduction to parameter estimation, fitting distributions, method of moments, examples.
Chapter 8.1 - 8.4
Sep 17
Examples of the method of moments. Maximum Likelihood Estimates (MLE)
Chapter 8.5

Solve Warmup and Practice Problems released on canvas

(Week 5) Parametric Estimation

Sep 22
Desirable properties of estimators: unbiasedness, consistency. The concept of UMVUE, Fisher Information, and Cramer-Rao Lower Bound (CRLB)
Chapter 8.7, 8.5.2
Sep 24
Proof of CRLB, Asymptotic Properties of MLE and other estimates, and confidence intervals
Chapter 8.5.2 - 8.5.3
Sep 16
HW 2 is due on Gradescope
HW 3 released on Canvas
Due on Oct 10.

(Week 6) Hypothesis Testing

Sep 29
The the delta method, Introduction to Bayesian Inference
Chapter 8.6
Oct 1
Credible Intervals, Introduction to hypothesis testing
Chapter 6.3, 9.1 - 9.2

(Week 7) Hypothesis Testing and Midterm Review

Oct 6
The Neyman-Prearson paradigm and optimal tests
Chapter 9.2
Oct 8
Midterm Review
Oct 10
HW 3 is due on Gradescope

(Week 8) Midterm 1

Oct 13
No class due to midterm break.
Oct 15
Midterm 1
In class, 11:30am - 1:00pm

(Week 9) Hypothesis Testing

Oct 20
Proof of the Neyman-Pearson lemma and composite hypotheses
Chapter 9.2
Oct 22
Generalized likelihood ratio tests
Chapters 9.4 and 6.3
Oct 24
HW 4 released on Canvas
Due on Oct 10. Gradescope

(Week 9) Hypothesis Testing

Oct 27
GLRT continued and the one-sample t-test, independence of sample mean and variance
Chapter 11.2 and 6.3
Oct 29
Inversions of tests to find confidence intervals, introduction to ordinary least squares
Chapters 14.1

(Week 11) Linear Regression

Nov 3
Ordinary least squares in one dimension, estimation
Chapter 14.2
Nov 5
OLS testing for dependence
Chapter 14.2
Nov 7
HW 4 is due on Gradescope
HW 5 released on Canvas
Due on Nov 21.

(Week 12) Categorical Data Analysis

Nov 10
The multinomial distribution, MLE, GLRT, Goodness of fit test
Chapters 8.5.1, 9.5 Nov 12
Contingency tables, odds ratio, test for independence
Chapters 13.1-13.4

(Week 13) Back to Estimation

Nov 17
Sufficiency, factorization theorem and examples
Chapter 8.8
Nov 19
Rao-Blackwell theorem to find UMVUEs and examples
Chapter 8.8
Nov 21
HW 5 is due on Gradescope
HW 6 released on Canvas
Due on Dec 14.

(Week 14) Midterm 2

Nov 24
Midterm 2
Nov 26
No class due to thanksgiving

(Week 15) Application of Statistical Methods

Dec 1
Bradley-Terry model
Nov 3
Poisson Regression Model

(Week 16) Final Review

Dec 8
Course review and looking ahead
Dec 10
No class due to finals week

(Week 17) Finals

Dec 14
HW 5 is due on Gradescope
Dec 16
Final Exam
In class, 1:30-3:30 pm