Stat 516A: Stochastic Modeling

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Stat 516 A: Stochastic Modeling of Scientific Data, Autumn 2009

Instructor:	Time and Place:
Vladimir Minin Padelford Hall C-315	Tuesdays and Thursdays 1:30-3:20 pm More Hall 220

Announcements:

10/05/09: homework 1 is online
10/02/09: lecture 1 is posted on the class discussion board
09/30/09: Please complete this short survey.

Course Description:
The purpose of this course is to introduce students to the art of stochastic modeling. The theoretical component of the course covers material standard for a first course in stochastic processes (see Karlin and Taylor, 1975). However, emphasis on statistical inference and scientifically motivated examples give a unique flavor to the mathematics presented in the course. The first quarter of the Stochastic Modeling sequence will be devoted to discrete and continuous-time Markov chains on countable state spaces and to statistical inference based on these models.

Course Description:

The purpose of this course is to introduce students to the art of stochastic modeling. The theoretical component of the course covers material standard for a first course in stochastic processes (see Karlin and Taylor, 1975). However, emphasis on statistical inference and scientifically motivated examples give a unique flavor to the mathematics presented in the course. The first quarter of the Stochastic Modeling sequence will be devoted to discrete and continuous-time Markov chains on countable state spaces and to statistical inference based on these models.

Textbook: none required.

Syllabus: syllabus_stat516.pdf

Lecture notes: updated regularly on the class discussion board

Homework assignments: post on class discussion board

Tentative Schedule:

Week 1	Examples of stochastic processes, probability background
Week 2	Intro to discrete-time Markov chains
Week 3	Hidden Markov models, properties, filtering, estimation
Week 4	One-step calculations, absorbing Markov chains
Week 5	Limiting behavior of Markov chains
Week 6	Statistical inference for discrete-time Markov chains
Week 7	Continuous-time Markov chains: construction
Week 8	Continuous-time Markov chains: properties, matrix exponentiation
Week 9	Inference for continuous-time Markov chains
Week 10	Partially observed continuous-time Markov chains

Reference Books:

P. Brémaud. Markov chains: Gibbs fields, Monte Carlo simulation, and queues, Springer, 1999.
P. Guttorp. Stochastic Modeling of Scientific Data, Chapman & Hall, 1995.
H.M. Taylor and S. Karlin. An Introduction to Stochastic Modeling, third edition, Academic Press, 1998.
S. Karlin and H.M. Taylor. A First Course in Stochastic Processes, second edition, Academic Press, 1975.
S. Karlin and H.M. Taylor. A Second Course in Stochastic Processes, Academic Press, 1981
K. Lange. Applied Probability, Springer, 2004.

Last modified: September 12, 2009