A Markov chain Monte Carlo (MCMC) simulation is a method of estimating an unknown probability distribution for the outcome of a complex process (a posterior distribution). Prior (capturing the concept

Monte Carlo (named for the casino in Monaco) methods estimate a distribution by random sampling. Many samples of the prior distributions must be obtained (e.g., many rolls of the dice) to obtain a stable and accurate posterior distribution. The modern version of the Monte Carlo was invented by Stanislaw Ulam and developed early on by John von Neumann and Nicholas Metropolis, the latter of whom suggested the name, as part of follow, on work to the Manhattan Project. Ulam was trying to calculate the probability of laying out a winning game of solitaire from a shuffled deck of 52 cards. Because of the complexity of the calculations, he decided it would be easier to play 100 games of solitaire and count the percentage that won.

In a Markov chain (named for Russian mathematician Andrey Markov [

Andrey Markov (1856–1922), photographer unknown, public domain,