Homepage > MCMC
Markov Chain Monte Carlo
  • Concept of Distribution
  • Monte Carlo Simulation
  • Markov Chain
  • Metropolis Algorithm
    Gibbs Sampler
  • Dynamics of Gibbs Models
  • Gibbs Distribution
  • Ising and Potts Models
    Statistical Models
  • Joint Distribution
  • Point Estimate
  • Bayesian Model
  • Mixture Model
  • MCMC scheme
    Explore MCMC with R
  • Normal Mixture
  • Searching for Maxima
  • Bernoulli Trials
  • Random Beta Walk
  • Metropolis Algorithm
  • Potts Model

    • Markov Chain Monte Carlo

    In Markov chain Monte Carlo (MCMC) one uses a Markov chain $ \mathbf{X}$ whose stationary distribution $ \pi$ is the distribution of interest. Then we run the chain $ \mathbf{X}$ for a long time $ t$ , then return $ \mathbf{X}_t$ . The chain is designed to be ``ergodic'' so that $ \mathbf{X}_t$ is ``approximately'' sampled from $ \pi$ when $ t$ is ``large enough'' we can sample. A standard construction of such a chain can be done via either (a) Metropolis-Hastings algorithm, or (b) Gibbs sampler. There is a large literature of theory and their applications available for MCMC. Here we list two useful sites to begin with:

    A short report will be asked for this special lecture. You can write anything, but should be able to justify some connection with this lecture. Or, you may find something to write about your own experimentation with R programming suggested in Explore MCMC with R. Submit electronically to mmachida@tntech.edu. Due July 23 (a week after the last meeting).

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