#### Statistics 251b/551b (Spring 1999)

# Stochastic Processes

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:** Tuesday 9:30--11:00 (or catch me straight after
a class)

**TA:** Andrew Carter

** Office hours:** Monday 2:30-3:30 (room 305 of 24 Hillhouse)

**Lectures:**
Monday, Wednesday 1:00 - 2:15 at WLH 207

### Prerequisites

A knowlege of elementary probability theory at the level of Statistics 241.
See some of my notes from 241 for a brief summary of facts about
conditional probabilities
and conditional expectations.
### Text

The course will be based on a
book manuscript being prepared by Joe Chang.
I expect to cover only the following topics from the
outline prepared by Joe:
- Markov chains
- Poisson processes
- Markov random fields and hidden Markov models
- Martingales
- Brownian motion

If time permits I might also cover parts of
- Diffusions, stochastic calculus, stochastic differential equations
- Likelihood ratios and extremes

### Grading

Most of the final grade will be based on the weekly homework assignments.
A small project will take the place of a final exam.

### Homeworks

Boxplots of homework scores.

Email correspondence regarding homeworks and
other aspects of the course.

Final projects

http://www.stat.yale.edu --->
Courses for
1998-99
---> Statistics 251
[MORE
COURSE INFORMATION]

*DBP 18apr99*