It was known from Metropolis et al. [J. Chem. Phys. 21 (1953) 1087--1092]that one can sample from a distribution by performing Monte Carlo simulationfrom a Markov chain whose equilibrium distribution is equal to the targetdistribution. However, it took several decades before the statistical communityembraced Markov chain Monte Carlo (MCMC) as a general computational tool inBayesian inference. The usual reasons that are advanced to explain whystatisticians were slow to catch on to the method include lack of computingpower and unfamiliarity with the early dynamic Monte Carlo papers in thestatistical physics literature. We argue that there was a deeper reason,namely, that the structure of problems in the statistical mechanics and thosein the standard statistical literature are different. To make the methodsusable in standard Bayesian problems, one had to exploit the power that comesfrom the introduction of judiciously chosen auxiliary variables and collectivemoves. This paper examines the development in the critical period 1980--1990,when the ideas of Markov chain simulation from the statistical physicsliterature and the latent variable formulation in maximum likelihoodcomputation (i.e., EM algorithm) came together to spark the widespreadapplication of MCMC methods in Bayesian computation.
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