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.
- 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
- The concept of UMVUE. Fisher Information, and Cramer-Rao Lower Bound (CRLB). Proof of CRLB, examples, and interpretation.
- Rice 8.7, 8.5.2
- Feb 11
- Practice Problems 4 posted on Canvas.
- Feb 12
- Asymptotic Properties of MLE and other estimates, and confidence intervals.
- Rice 8.5.2 - 8.5.3
(Week 7) Estimation
- Feb 17
- The delta method. Introduction to Bayesian parametric inference
- Wasserman 5.5 and 9.9., Rice 8.7
- Feb 19
- Quiz 3 in class
Lab 3 in class on simulations related to CRLB, asymptotics of MLE, Bayes estimates etc.
Coding assignment 1 is due on gradescope.
- Feb 20
- Practice Problems 5 posted on Canvas.
(Week 8) Midterm 1
- Feb 24
- Midterm Review.
- Feb 26
- Midterm 1
- In class, 2:30pm - 4:00pm
(Week 9) Hypothesis Testing
- Mar 10
- Introduction to Hypothesis Testing, Type-I and Type-II errors, power of a test
- Chapter 6.3, 9.1 - 9.2
- Mar 12
- The Neyman-Pearson Paradigm and composite hypothesis
- Rice 9.2
(Week 9) Hypothesis Testing
- Mar 17
- Proof of the Neyman-Pearson Lemma, Generalized Likelihood Ratio Test (GLRT)
- Rice 9.2, 9.4
- Mar 19
- GLRT continued
- Chapter 11.2 and 6.3
Lab 4 in class on hypothesis testing.
(Week 11) Hypothesis Testing and Linear Regression
- Mar 24
- One sample t-test. Independence of sample mean and variance for Gaussians.
- Rice 11.2 and 6.3
- Mar 26
- Introduction to ordinary least squares in one dimension, estimation
- Chapter 14.2
Quiz 4 in class
(Week 12) Linear Regression
- Mar 31
- OLS testing for dependence
- Rice 14.2
- Apr 2
- The multinomial distribution, MLE, GLRT, Goodness of fit test
- Rice 8.5.1, 9.5
(Week 13) Categorical Data
- Apr 7
- Contingency tables, odds ratio, test for independence
- Rice 13.1-13.4
- Apr 9
- Quiz 5 in class
Lab 5 in class.
(Week 14) Categorical Data
- Apr 14
- Sufficiency, factorization theorem and examples
- Rice 8.8
- Apr 16
- Rao-Blackwell theorem to find UMVUEs and examples
- Rice 8.8
(Week 15) Course Review
- Apr 21
- Course review and looking ahead
- Apr 23
- No class due to study break
(Week 16) Final Week
- Apr 29
- Final Exam
- In class, 1:30pm - 3:30pm