| 36-752, Spring 2018 Class Schedule | Date | Lecture Topic | Readings | Scribe Notes | Notes |
|---|---|---|---|---|
| Jan 16, T | No class | |||
| Jan 18, R | No class | |||
| Jan 23, T | No class | |||
| Jan 25, R | No class | |||
| Jan 30, T | Course overview. Basic Set Theoretic Concepts. Sigma-fields. | Lecture notes: Set 1 | Natalia | |
| Feb 1, R | Measure. Sigma-Finiteness. Continuity of measure. Uniqueness (pi-lamba theorem) | Lecture notes: Set 1 | Riccardo |
Here is an example of a non-measurable set. From Billingsley, page 45. HW1 is out. Solutions to HW1. |
| Feb 6, T | Carathedory extension thorem. Measures from distribution functions. Measurable functions and random variables. | Lecture notes: Set 2 | Ron | |
| Feb 8, R | Measurable functions and random variables. Integration. | Lecture notes: Set 3 | Theresa | |
| Feb 13, T | Integral. Fatou's Lemma and Monotone Convergence Theorem. | Lecture notes: Set 3 | Shamindra | To compare the Lebesgue vs Riemann integral, see, e.g., this excerpt from the book "Mathematical Analysis", by Apostol, Addison Wesley (1981) |
| Feb 15, R | Dominated convergence theorem. Densities. Product Measure. | Lecture notes: Set 3 and 4 | Yue | HW2 is out. Solutions to HW2. |
| Feb 20, T | Product Measure. | Lecture notes: Set 4 | Yifan | |
| Feb 22, R | Product Measure (cont'd). Lp spaces. | Lecture notes: Set 4, 5 and 6. | Heejong | |
| Feb 27, T | Lp spaces (cont'd) and Conditional Expectation. | Lecture notes: Set 5 and 6. | Matteo | |
| Mar 1, R | Conditional Expectation. Regular Conditional Probabilities. | Lecture notes: Set 6. |
Wanshan Billingsley's take on conditional probabilities. |
HW3 is out. Solutions to HW3. |
| Mar 6, T | Regular Conditional Probabilities. Martingales. | Lecture notes: Set 6 and 7. |
Pratik |
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| Mar 8, T | Martingales. Stopping Times. | Lecture notes: Set 7. | ||
| Mar 13, T | Spring Break. | |||
| Mar 15, T | Spring Break. | |||
| Mar 20, T | Optional Stopping Theorem. Convergence in Probability | Lecture notes: Set 7 and 8. |
Maria |
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| Mar 22, R | Convergence in Probability, in mean and almost surely | Lecture notes: Set 8 and 9. |
Trey |
HW4 is out. Solutions to HW4. |
| Mar 27, T | Relationship between convergence in probability, law and almost surely. Borel-Cantelli Lemmas. | Lecture notes: Set 8 and 9. |
Riccardo |
|
| Mar 29, R | SLLN and converence in distribution. | Lecture notes: Set 9 and 10. |
Natalia |
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| Apr 3, T | Convergence in distribution. Portmanteau and Continuous Mapping Theorem | Lecture notes: 10. | ||
| Apr 5, R | Continuous Mapping Theorems, Slutsky Theorems. | Lecture notes: 10. |
Wanshan |
HW5 is out. Solutions to HW5. |
| Apr 10, T | Op and op notation. Delta Method. | Lecture notes: 10. | ||
| Apr 12, R | CLT. | Lecture notes: 11. |
Theresa |
|
| Apr 17, T | Berry Esseen bound, CLT in high dimesnions. | Lecture notes: 11. |
Heejong |
|
| Apr 19, R | No class (CMU Carnival). | |||
| Apr 24, T | Efficient Lieklihood Estimation. | Chapter 4 of Jon Wellner's notes. |
Ron |
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| Apr 26, R | Efficient Lieklihood Estimation. | Chapter 4 of Jon Wellner's notes. | ||
| May 1, T | Concentration of measure in high dimensions. | See references webpage for a list of sources on this topic. |
Yifan |
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| May 3, R | Concentration of measure in high dimensions. | See references webpage for a list of sources on this topic. | ||