Statistics 251/551 (Spring 2009)
||Mon, Wed 1:00 - 2:15
| Office hours:
|| after each class, and Thursday 12:30-1:30
||to be arranged if needed
Introduction to the study of random processes, including Markov chains, Markov random fields, martingales, random walks, Brownian motion and diffusions. 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.
The course is aimed at students (both graduate and
undergraduate) who are comfortable with introductory
probability (as covered in Stat 241/541).
The course will be based on a book manuscript written by Joe Chang. I will take some material from each chapter. I will post supplementary notes if I deviate too far from Joe's treatment of any topic.
Basic theory for Markov Chains with finite or countable state spaces: transition probabilities; periodicity; transience and recurrence; stationary distributions; convergence to stationary distributions. [Chang Chapters 1 and 2]
Markov random fields [Chang Chapter 3]
Martingales [Chang Chapter 4]
Brownian Motion and Diffusion [Chang Chapters 5 and 6]
The final grade will be based on the weekly homework plus two take-home exams.
Students who wish to work in teams (no more than 2 to a team)
should submit a single a solution set. All members of a team will be
expected to understand the team's solutions sufficiently well to
explain the reasoning at the blackboard. Occasional meetings with DP
will be arranged.
Homework due each Monday.
Class materials for an introductory probability course
Fall 2005), containing more extensive elementary discussion of
See, in particular, the first two chapters, on (conditional) probability and (conditional) expectations.