Course Material
| Date |
Material Covered |
Reading Material |
Homework |
Due date |
Solution |
| September 24 |
Course outline and organization |
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| September 29 |
Decision theoretic framework for inference |
Section 1.1, 1.2 |
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| October 1 |
Bayes and minimax rules, an illustration when
the parameter space is finite |
Section 1.3 |
Homework 1 |
October 8 |
Solution key |
| October 6 |
Introduction to measure theory : sigma-fields, measures |
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| October 8 |
Integrals of functions; Radon-Nikodym theorem |
Measure Theory notes |
Homework 2 |
October 16 |
Solution key |
| October 13 |
Random variables and their distributions; Product measure |
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| October 15 |
Independent random variables; Conditional expectation and conditional
probability distribution |
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Homework 3 |
October 23 |
Solution key |
| October 20 |
Moment generating function, Characteristic function,
Multivariate normal distribution |
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| October 22 |
Transformation of random variables,
Gamma distribution, Beta distribution |
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Homework 4 |
October 30 |
Solution key |
| October 27 |
Order statistics; Sufficiency |
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| October 29 |
Exponential family of distributions |
Section 1.5, 1.6 |
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| November 3 |
Exponential family (continued) |
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| November 5 |
Midterm |
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| November 10 |
Conjugate family of priors; Bayes rule |
Section 3.2 |
Homework 5 |
November 17 |
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| November 12 |
Minimax procedures as Bayes or limits of Bayes procedures |
Section 3.3 |
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| November 17 |
Completeness, UMVUE |
Section 3.4 |
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| November 19 |
Rao-Blackwell theorem, Fisher information |
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Homework 6 |
December 2 |
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