Efficient Monte Carlo Methodology
Monte Carlo methods have proven an enormously valuable tool over
the last 60 years for statisticians finding p-values, physicists
modeling complex systems, computer scientists approximating #P-complete
problems, Bayesian analysts learning about posterior distributions,
material sciences, genetic analysis and other areas. This course will
cover two classes of methods for building Monte Carlo methods. The
first is Markov chain Monte Carlo. The three major types of Markov
chains: Metropolis-Hastings, Gibbs/slice sampling, and
auxilliary/latent variable chains will be described, applied to
applications, and when possible analyzed to determine their
effectiveness. The second class of methods are perfect sampling
methods. The major types of methods here are acceptance/rejection,
coupling from the past, popping, the randomness recycler, and partial
recursion acceptance/rejection. The class will be roughly 50/50
applications and theory. |
