Encyclopedia of Applied and Computational Mathematics

2015 Edition
| Editors: Björn Engquist

Bayesian Statistics: Computation

  • Martin A. Tanner
Reference work entry
DOI: https://doi.org/10.1007/978-3-540-70529-1_327

Mathematics Subject Classification

62F15; 65C40


Markov chain Monte Carlo (MCMC)

Short Definition

Markov chain Monte Carlo (MCMC) is a collection of computational methods for simulating from posterior distributions.


Markov chain Monte Carlo (MCMC) methods are a collection of computational algorithms designed to sample from a target distribution by performing Monte Carlo simulation from a Markov chain whose equilibrium distribution is equal to the target distribution. The output of the algorithm is then used to estimate features of the required distribution, where the quality of the estimate is determined by the number of iterations of the algorithm. Surprisingly, it took several decades before the statistical community embraced Markov chain Monte Carlo (MCMC) as a general computational tool in Bayesian inference, where it may be quite difficult to compute the normalizing constant of the (possibly high-dimensional) posterior distribution required for routine...

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Martin A. Tanner
    • 1
  1. 1.Department of StatisticsNorthwestern UniversityEvanstonUSA