| Date | Topics |
|---|---|
| Week 1 (Jan.14) | Conditional probability and conditional expectations: review (3.1-3.3) |
| Week 2 (Jan.21) | Computing probabilities, expectations by conditioning. Markov chain basics: (2.8,3.4,3.5, 4.1) |
| Week 3 (Jan.28) | Gambler's ruin, Chapman-Kolmogorov Equations, Classification of states (4.2,4.3) |
| Week 4 (Feb.4) | Recurrence, Ergodic theorem, limiting probabilities (4.4, 4.5) |
| Week 5 (Feb.11) | Reversibility, Ehrenfest Model, Branching Processes (4.8) |
| Week 6 (Feb.18) | Poisson Processes (5.1-5.3) |
| Week 7 (Feb.25) | more on Poisson Processes. Continuous-time Markov chain basics. |
| Week 8 (Mar.3) | Continuous-time Markov chains, birth-death processes. Midterm exam on Wednesday, March 5th |
| Week 9 (Mar.10) | Spring break |
| Week 10 (Mar.17) | I.i.d. Monte Carlo: basic theory (handouts, 11.1, 11.2.1, 11.2.2) |
| Week 11 (Mar.24) | Rejection sampling, Importance sampling (handouts) |
| Week 12 (Mar.31) | Importance sampling |
| Week 13 (Apr.14) | Markov chain Monte Carlo (MCMC): basic theory. The Metropolis-Hastings/Gibbs samplers |
| Week 14 (Apr.21) | M-H variants, MCMC implementation issues |
| Week 15 (Apr.28) | MCMC for maximum likelihood estimation. Extra topics, review Take home final due Monday, April 28th. |
| Week 16 (May.5) | Final exam: Monday, May 5 8:00A-9:50A, 220 THOMAS |