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Abstract

The breakthrough to be discussed here occurred in two steps, separated in time by over three decades. The first, conceptually decisive step, but lacking direct relevance to mainstream statistics, was the invention of Markov Chain Monte Carlo methods by Metropolis et al. (1953). The second step, decisive for applications in statistics, occurred when Geman and Geman (1984) wrestled the seminal idea of Metropolis et al. from its statistical mechanics surroundings, modified it, and applied it to Bayesian modeling and the computation of posterior distributions in otherwise intractable situations.