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Pseudo-marginal Metropolis–Hastings algorithm
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<p>In <a href="/facts/Computational_statistics/noW2SBX8">computational statistics</a>, the pseudo-marginal Metropolis–Hastings algorithm is a <a href="/facts/Monte_Carlo_method/AkHjY7jc">Monte Carlo method</a> to sample from a probability distribution. It is an instance of the popular <a href="/facts/Metropolis%E2%80%93Hastings_algorithm/8K7bz3LN">Metropolis–Hastings algorithm</a> that extends its use to cases where the target <a href="/facts/Probability_density_function/zvfybna4">density</a> 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 <a href="/facts/Bayesian_statistics/9w7b1Bw4">Bayesian statistics</a>, where it is applied if the <a href="/facts/Likelihood_function/1L8P4NBX">likelihood</a> function is not tractable (see example below). </p>