Editing Markov chain Monte Carlo (section)

{{Short description|Calculation of complex statistical distributions}}
{{Bayesian statistics}}
In [[statistics]], '''Markov chain Monte Carlo''' ('''MCMC''') is a class of [[algorithm]]s used to draw samples from a [[probability distribution]]. Given a probability distribution, one can construct a [[Markov chain]] whose elements' distribution approximates it – that is, the Markov chain's [[Discrete-time Markov chain#Stationary distributions|equilibrium distribution]] matches the target distribution. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution.

Markov chain Monte Carlo methods are used to study probability distributions that are too complex or too highly [[N-dimensional space|dimensional]] to study with analytic techniques alone. Various algorithms exist for constructing such Markov chains, including the [[Metropolis–Hastings algorithm]].