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
    Bayesian Models
  • Joint Distribution
  • Frequentist Approach
  • Bayesian Approach
  • Dirichlet Distribution
  • Mixture Model
  • MCMC scheme
    Data Mining and MCMC
  • Relative Report Rate
  • Graphical 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:

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