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Education and Training: Introduction to Markov Chains: Markov Chain Monte Carlo for Scientists & Engineers

Time and Location Introduction to Markov Chains: Markov Chain Monte Carlo for Scientists & Engineers
Andrew Rukhin, Stefan Leigh and Van Molino
Statistical Engineering Division, NIST
MondayTeusday August 16/17 2004, 9:00 am-4:30pm
Administration Building, Lecture Room B
Abstract The concept of Markov Chains was first introduced by A.A. Markov in 1906, in a paper extending the Law of Large Numbers and Central Limit Theorem to a weakly - Markovianly - dependent sequence of random variables. The importance of the work was recognized early on, and advances were made quickly in the generalization of the Markovian structure to processes with countably infinite and continuum state spaces and continuous time. As the theory evolved, its application to the physical, biological, and social sciences evolved as well. The corpus of work that resulted for the finite state space/discrete time case seemed so complete, that by the 1960's the area was regarded as essentially unamenable to any breakthrough research.

Little attention was paid to an obscure paper (Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller) in the Journal of Chemical Physics in 1953. But over several subsequent decades, the idea introduced there, that one can employ a finite state discrete time Markov chain to describe multiple important combinatoric and physical phenomena, and exercise the chain efficiently to derive limiting behavior, caught fire. In the 1990's, the technique, dubbed (MC)2, took off, and has emerged as one of the single most important techniques for simulating complex mathematical and physical phenomena.

In this introductory course, we devote one day to the exploration of finite Markov Chains and their applications, and one day to their application to (MC)2. This is not a "proof" course. Our exposition relies heavily on examples drawn from multiple disciplines. Prerequisites include basic notions of probability and matrices, which will be reviewed briefly at the start of the course.

Comments on Course REGISTRATION FEE IS $75.

A set of notes will be provided for the class, and a textbook (Olle Haggstrom, Finite Markov Chains and Algorithmic Applications) will be provided.

The class size is limited to 20 students.

Further Information For further information, contact or register online (once the course is scheduled) at http://www-i.nist.gov/cgi-bin/training.cgi

Date created: 7/15/2004
Last updated: 7/15/2004
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