The use of Markov chain Monte Carlo (MCMC) methods to evaluate integral quantities

has exploded over the last two decades. Beginning with the seminal review paper by Gelfand

and Smith (1990), the rate of publication of MCMC works has grown exponentially. While

this is relatively a recent development, the genesis dates back to two important works: the

1953 essay by Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller, as well as Geman

and Geman’s (1984) introduction of the Gibbs sampler as a method for obtaining difficult

posterior quantities in the process of image restoration. The lack of early recognition of

the importance of the 1953 contribution is a testament to the barriers that may exist

between statistical physics and other fields, and the hindsight that sufficiently powerful

computational resources were not widely available until sometime afterwords. This history

is nicely reviewed by Robert and Casella (2011), as well as by Richey (2010). Another

fundamental tool in this family is simulated annealing (Kirkpatrick, Gelatt, and Vecchi

[1983], Cˇerny´ [1985]), which is described at the begining of Chapter 15.