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

    This presentation (http://math.tntech.edu/machida/MCMC/) has been developed for a series of lectures in Summer 2008 at Tokyo Institute of Technology. Markov chain Monte Carlo (MCMC) becomes an indispensable methodology when it is intractable to sample directly from the distribution of interest. In MCMC one designs a Markov chain whose stationary distribution is the one we seek, and implements a computer algorithm to run a sample path from the Markov chain. We begin our discussion with the concept of Monte Carlo simulation and Markov chains, which enables us to investigate MCMC methods and their algorithms. The presentation is also interspersed with demonstrations in R (which is free software/platform for statistical computing and graphics), and the source code is made available for anyone interested in running it. Here we cover the following three topics:
    1. Introduction to Monte Carlo simulation, Markov chains, and MCMC.
    2. MCMC algorithms: Taking advantage of Markov chains.
    3. Bayesian computation and data mining: MCMC in practice.
    There are a large number of expository and research papers on MCMC methods and their applications. Quite a few of them are made available at

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