Functional Compatibility, Markov Chains, and Gibbs Sampling with Improper Posteriors

On sampling with Markov chains

Exact Sampling with Markov Chains

Random sampling has found numerous applications in computer science, statistics, and physics. The most widely applicable method of random sampling is to use a Markov chain whose steady state distribution is the probability distribution r from which we wish to sample. After the Markov chain has been run for long enough, its state is approximately distributed according to 7r. The principal proble...

Markov Chain Monte Carlo and Gibbs Sampling

A major limitation towards more widespread implementation of Bayesian approaches is that obtaining the posterior distribution often requires the integration of high-dimensional functions. This can be computationally very difficult, but several approaches short of direct integration have been proposed (reviewed by Smith 1991, Evans and Swartz 1995, Tanner 1996). We focus here on Markov Chain Mon...

Markov Chain Monte Carlo and Gibbs Sampling

A major limitation towards more widespread implementation of Bayesian approaches is that obtaining the posterior distribution often requires the integration of high-dimensional functions. This can be computationally very difficult, but several approaches short of direct integration have been proposed (reviewed by Smith 1991, Evans and Swartz 1995, Tanner 1996). We focus here on Markov Chain Mon...

From Markov Chains to Gibbs Fields