Markov chain Monte Carlo (MCMC)

Development of the Markov chain Monte Carlo (MCMC) methods (see, for example, Robert and Casella 2013,, and the rapid increase in computational power even in standard personal computers in the 1990’s have  allowed researchers to apply Bayesian inference more easily and more flexibly than before. The MCMC methods generate a random sample approximating a random sample from a probability distribution. The distribution can be high-dimensional, thus the MCMC methods suit well to Bayesian inference. WinBugs and later OpenBugs and JAGS have been introduced as easy-to-use and flexible tools using the MCMC to build Bayesian models with a fixed parameter space. The reversible jump MCMC (RJMCMC; Green 1995) was another breakthrough in the 1990’s allowing Bayesian models without fixing the dimension of the parameter space.

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