Class Schedule
(Week 1) Recap of Probability Theory
- Sep 1
- (Lecture 1) Random Variables, Distributions, Expectation, Variance, Inverse CDF, Moment Generating Functions (MGF)
- Rice, Chapter 2 and 4
- Sep 3
- (Lecture 2) 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).
- Sep 3
- Practice Problem 1 released on Canvas
(Week 2) Recap of Probability Theory
- Sep 8
- (Lecture 3) Variance, Covariance, Correlation, the multivariate Gaussian distribution
- Rice 6.2 (review Rice 3.2-3.3, 4.3 if necessary)
- Sep 9
- Solution to Practice Problems 1 posted on canvas
- Sep 10
- (Lecture 4) Asymptotics and Simulations
- Rice, Chapter 5.1-5.3
- Lab 1 on simulation of LLN and CLT
(Week 3) Introduction to Estimation
- Sep 15
- (Lecture 5) Introduction to Parametric Estimation
- Rice 8.1.
- Quiz 1 in class
- Sep 17
- (Lecture 6) Introduction to parameter estimation, fitting distributions, method of moments, examples, intro to MLEs.
- Rice 8.1 - 8.5
- Practice Problems 2 posted on canvas
(Week 4) Parametric Estimation
- Sep 22
- (Lecture 7) Examples of the method of moments. Maximum Likelihood Estimates (MLE)
- Rice 8.5
- Sep 24
- (Lecture 8) Desirable properties of estimators: unbiasedness, consistency.
- Rice 8.7, 8.5.2
(Week 5) Parametric Estimation
- Sep 29
- (Lecture 9) Fisher Information. Asymptotic Properties of MLE and confidence intervals.
- Rice 8.5.2 - 8.5.3
- Quiz 2 released.
- Oct 1
- Practice Problems 4 posted on Canvas.
- Oct 1
- (Lecture 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
- Lab 2 in class.
- Coding Assignment 1 released.
- Due on Oct 11.
(Week 6) Estimation
- Oct 6
- (Lecture 11) CRLB continued
- Rice 8.7. :
- Oct 8
- (Lecture 12) Introduction to Bayesian parametric inference
- Rice 8.6
(Week 7) Bayesian Inference
- Oct 13
- (Lecture 13) Bayesian parametric inference continued
- Rice 8.7.
- Quiz 3 in class
Lab 3 in class.
- Oct 15
- (Lecture 14) Midterm Review
(Week 8) Midterm
- Oct 20
- No class due to midterm break.
- Oct 22
- Midterm 1
- In class, 2:30pm - 4:00pm
(Week 9) Hypothesis Testing
- Oct 27
- (Lecture 15) Introduction to Hypothesis Testing, Type-I and Type-II errors, power of a test
- Chapter 6.3, 9.1 - 9.2
- Oct 29
- (Lecture 16) The Neyman-Pearson Paradigm and composite hypothesis
- Rice 9.2
- Practice Problems 6 released on Canvas.
(Week 10) Hypothesis Testing
- Nov 3
- (Lecture 17) Proof of the Neyman-Pearson Lemma, Generalized Likelihood Ratio Test (GLRT)
- Rice 9.2, 9.4
- Nov 5
- (Lecture 18) GLRT continued. Derivation of the t-test. Independecne of sample mean and variance.
- Chapter 11.2 and 6.3
(Week 11) Categorical data
- Nov 10
- (Lecture 19) Finishing off the proof of independence between sample mean and variance.
- Rice 8.5.1.
- Lab 4 in class
- Nov 12
- (Lecture 20) Introduction to categorical data. the multinomial distribution, MLE through Lagrange multipliers.
- Rice 13.1 - 13.3
- Quiz 4 in class
(Week 12) Categorical Data
- Nov 17
- (Lecture 22) MLE under the restricted setup, Hardy-Weinberg Equilibrium Example, GLRT, and Chi-squared tests.
- Rice 9.5, 13.4
- Nov 19
- (Lecture 23) Test for independence and homogeneity.
- Rice 13.1 - 13.4.
(Week 13) Categorical Data and Introduction to Sufficiency
- Nov 24
- (Lecture 24) Introduction to Sufficiency.
- Quiz 5 in class
8.8
- Nov 26
No class. Happy Thanksgiving!
(Week 14) Categorical Data
- Dec 1
- (Lecture 25) Sufficiency, factorization theorem and examples
- Rice 8.8
- Dec 3
- (Lecture 26) Rao-Blackwell theorem to find UMVUEs and examples
- Rice 8.8
(Week 15) Course Review
- Dec 8
- (Lecture 27) Examples
- Dec 10
- (Lecture 28) Course review and looking ahead
(Week 16) Final Week
- Dec 18
- Final Exam
- In class, 4:00pm - 6:00pm