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An Introduction to Markov Chain Monte Carlo

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Instructor:
Prof. Carlos C. Rodriguez
Office Hours:
Tues., Wed. and Thurs. after lectures or by appointment on Weds..
Text:
Radford M. Neal, 1993. Probabilistic Inference Using Markov Chain Monte Carlo Methods. Available online at http://omega.albany.edu:8008/neal.pdf and http://omega.albany.edu:8008/neal-review.ps

Topics

Week 1
Introduction and overview of some applications: e.g. Computation of Integrals, Combinatorial Optimization, Bayesian Inference, Density Estimation.

Non Uniform Random Variate Generation by Computer: Inverse cdf method, rejection methods, specialized methods.

Week 2
Overview of the theory of Markov Chains: Basic definitions, Invariant Distributions, Ergodicity, Reversibility, Continuous Time Chains, Coupling, examples.

Week 3
Metropolis, Gibbs and Simulated Annealing methods. Definitions, Convergence Theorems, examples.

Week 4
The Dynamical and Hybrid Monte Carlo Methods. Quick overview of Hamiltonian Systems and their use in MCMC.

Week 5
Propp and Wilson Algorithm and Perfectly Random Sampling with Markov Chains. Basic Proofs and overview of current literature.

EVALUATION
Based on attendance and on a computer project assigned individually during the first week of class and due before the end of the course.


File translated from TEX by TTH, version 1.95.
On 7 Jun 1999, 16:53.