Pseudo-marginal Metropolis–Hastings algorithm

The Pseudo-marginal Metropolis-Hastings (PMMH) algorithm is a Markov Chain Monte Carlo (MCMC) method used for sampling from complex posterior distributions, particularly in Bayesian inference settings. It is especially useful when the likelihood function is intractable or computationally expensive to evaluate directly. ### Overview In standard MCMC methods, a proposal distribution is used to explore the parameter space, and the acceptance criterion is based on the ratio of the posterior probabilities.