A study of random processes, including Markov chains, Markov random fields, martingales, random walks, Brownian motion and diffusions. Introduction to certain modern techniques in probability such as coupling and large deviations. Applications to image reconstruction, Bayesian statistics, finance, probabilistic analysis of algorithms, genetics and evolution. After Statistics 241a or equivalent.
Instructor: David Pollard
(24 Hillhouse Avenue;
david.pollard@yale.edu)
Office hours: Tuesdays 11:00 -- 12:00, or by appointment
TA: Anna Kotchetkova
Office hours: TBA
Lectures: Monday, Wednesday 1:00 - 2:15
Where: 102 Becton center (15 Prospect St)
Week starting | Monday | Wednesday | Homework |
---|---|---|---|
12 Jan | Overview. Read JC §1.1, §1.2 | Some examples of MCs. | |
19 Jan | Classification of states | Stationary distributions | #1 due ?? |
26 Jan | Behavior of a MC during a cycle | Positive recurrence | |
2 Feb | Basic limit theorem | The Metropolis method | |
9 Feb | Simulated annealing ... | ... continued | |
16 Feb | Card shuffling | Martingales | |
23 Feb | Optional sampling of martingales | Option pricing in discrete time | |
1 Mar | Convergence of positive supermartingales | Branching processes | |
8 & 15 Mar | spring break | ||
22 Mar | Brownian motion | Reflection principle; Ornstein-Uhlenbeck | |
29 Mar | Sample paths of Brownian motion; quadratic variation; diffusions | Ito stochastic integral | |
5 Apr | |||
12 Apr | |||
19 Apr |
DBP 6jan04