**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

**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.

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 T

On 7 Jun 1999, 16:53.