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The burn-in period consists of the initial samples generated by an MCMC algorithm before it has converged to its stationary distribution. These samples must be discarded because they are influenced by the arbitrary starting point and do not accurately represent the target distribution.

Conditions: Applies to MCMC sampling.; Requires discarding initial samples before using the rest for inference.; The chain starts from an arbitrary point.

The burn-in period consists of the initial samples generated by an MCMC algorithm before it has converged to its stationary distribution. These samples must be discarded because they are influenced by the arbitrary starting point and do not accurately represent the target distribution.

Conditions: Applies to MCMC sampling.; Requires discarding initial samples before using the rest for inference.; The chain starts from an arbitrary point.

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 $\pi$.