Bayesian Computation Using Markov Chain Monte Carlo Methods

Iterative simulations such as Markov chain Monte Carlo (MCMC) have made it possible to fit complex and more realistic Bayesian models to large and/or incomplete datasets. However, there are still many open questions in using (MCMC) methods. Our research program in this field features the following aspects:

  1. (Over-dispersed) Starting Distribution and Convergence Diagnostics
    Gelman and Rubin (1992) noticed the importance of running multiple MCMC chains for obtaining reliable statistical inferences. Chuanhai Liu and Donald B. Rubin are continuing their work on "Markov Analysis of Iterative Simulations Before Their Convergence" (Liu and Rubin, 1996), which can be used to create an overdispersed starting distribution for running multiple chains.
  2. Efficient MCMC Algorithms

    We have developed several efficient MCMC algorithms:

  3. Applications

    MCMC methods have been applied to many projects within the Statistical Research Department at Bell Labs. For example,

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