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The stationary distribution is a probability distribution that remains unchanged as the Markov chain evolves. It is important for MCMC because when the chain reaches equilibrium, the long-run fraction of time spent in each region exactly matches the target probability, allowing the chain to act as a perfect sampler.

Conditions: The Markov chain must reach equilibrium.; $\pi$ is a probability vector and $P$ is the transition matrix.; The target distribution is $\pi$.

The stationary distribution is a probability distribution that remains unchanged as the Markov chain evolves. It is important for MCMC because when the chain reaches equilibrium, the long-run fraction of time spent in each region exactly matches the target probability, allowing the chain to act as a perfect sampler.

Conditions: The Markov chain must reach equilibrium.; $\pi$ is a probability vector and $P$ is the transition matrix.; The target distribution is $\pi$.