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About: Pseudo-marginal Metropolis–Hastings algorithm     Goto   Sponge   NotDistinct   Permalink

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In computational statistics, the pseudo-marginal Metropolis–Hastings algorithm is a Monte Carlo method to sample from a probability distribution. It is an instance of the popular Metropolis–Hastings algorithm that extends its use to cases where the target density is not available analytically. It relies on the fact that the Metropolis–Hastings algorithm can still sample from the correct target distribution if the target density in the acceptance ratio is replaced by an estimate. It is especially popular in Bayesian statistics, where it is applied if the likelihood function is not tractable (see example below).