# Markov Chain Monte Carlo (MCMC)

An iterative approach to generate samples from some target distribution $$\pi$$ defined on a state space $$\mathcal{X}$$ by constructing a Markov Chain which has $$\pi$$ as its stationary distribution.

MCMC is often used in Bayesian modelling where we want to sample from the posterior distribution, which is often known up to a normalizing constant.

The time it takes to reach the stationary distribution $$\pi$$ is called the mixing time. Since initial samples are not from $$\pi$$ they are thrown away.

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Created: 2022-04-04 Mon 23:40

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