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