Date | Topic | Notes |
---|---|---|
Tu, Sept 6 | Introduction | |
Th, Sept 8 | Sample spaces, probability functions; conditional probability, Bayes' rule, independence; discrete vs. continuous random variables; transformation formulas | Due for Thursday Sept. 15: Exercises 1 and 2 from the lecture notes. |
Tu, Sept 13 | means, variances; joint, conditional, marginal distributions | |
Th, Sept 15 | correlation, covariance; moment-generating functions, convolution | Due for Thursday Sept. 22: Exercises 4, 5, 6, 8, 9, 11, 14, 15 from the lecture notes. |
Tu, Sept 20 | special distributions: binomial, Gaussian (normal), Poisson, uniform, exponential, etc. | |
Th, Sept 22 | probability inequalities: Markov, Chebysheff, Chernoff, Jensen, Cauchy-Schwarz. Convergence in probability and distribution. Law of large numbers. | Due for Thursday Sept. 29: Exercises 17, 18, 21, 23, 24, 25, 26, 27 from the lecture notes. |
Tu, Sept 27 | Central limit theorem, delta method |
Date | Topic | Notes |
---|---|---|
Th, Sept 29 | loss functions, expected loss, worst-case vs. average risk; domination + admissibility of decision rules | Due for Thursday Oct 6: Exercises 31, 32, 33, 36, 37, 39 from the lecture notes. |
Date | Topic | Notes |
---|---|---|
Tu, Oct 4 | Bayes estimators, bias and variance, bias-variance decomposition, unbiased, minimum-variance estimators | |
Th, Oct 6 | Maximum likelihood estimation | Quiz today: on material covered in HW sets 1-3. Due for Thursday Oct 13: Exercises 40, 42, 43, 44, 45, 50 from the lecture notes. |
Tu, Oct 11 | More on MLE | |
Th, Oct 13 | Sufficient statistics | Due for Thursday Oct 20: Exercises 51-54, 57, 58, 60, 61 from the lecture notes. |
Tu, Oct 18 | Minimal sufficiency; Rao-Blackwell theorem | |
Th, Oct 20 | Exponential families | Due for Thursday Oct 27: Exercises TBA from the lecture notes. (Just kidding, take a break.) |
Tu, Oct 25 | Midterm review | Come with questions! |
Th, Oct 27 | Midterm | On material covered in HW sets 1-6 (HW 6 was the one that was due on Oct. 20). Due for Thursday Nov 3: Exercises 62, 64-71 from the lecture notes. |
Tu, Nov 1 | Midterm post mortem | |
Th, Nov 3 | More on exponential families | Due for Thursday Nov 10: Exercises 73, 75-79 from the lecture notes. |
Tu, Nov 8 | No class (holiday) | Vote. |
Th, Nov 10 | Asymptotics of estimation: consistency, method of moments, confidence intervals | Due for Thursday Nov 17: Exercises 83-87 from the lecture notes. |
Tu, Nov 15 | Consistency of the MLE | Quiz today: on sufficiency and exponential families |
Th, Nov 17 | More MLE asymptotics: Fisher information | Due for Thursday Dec 1: Exercises 88-95 from the lecture notes. |
Tu, Nov 22 | Cramer-Rao bound, asymptotic efficiency | Happy Thanksgiving |
Date | Topic | Notes |
---|---|---|
Tu, Nov 29 | Simple hypotheses: ML tests; power, size; Neyman-Pearson lemma | |
Th, Dec 1 | Compound alternate hypotheses; uniformly most powerful tests | Due for Thursday Dec 8 (last homework!): Exercises 99-101, 107, 108, and 110-113 from the lecture notes. |
Tu, Dec 6 | Compound null and alternate; t-tests; likelihood ratio test in compound case | |
Th, Dec 8 | Exam review (optional) | Bring questions! |
Tu, Dec 13 | Exam review (optional) | Bring questions! |
Th, Dec 15 | Exam (not optional) | At the usual time and place. |