Particle Mean Field Variational Bayes

To solve this problem, there are two main classes of computational methods that provide different approaches to approximate π. The first one is Markov chain Monte Carlo (MCMC) methods (Metropolis et al., 1953; Hastings, 1970; Robert and Casella, 1999). For many years, MCMC has been the standard approach for Bayesian analysis because of its theoretical soundness. The method constructs a Markov chain to produce simulation consistent samples from the target distribution π. A general MCMC approach is the Metropolis-Hastings algorithm that generates a Markov chain by first generating a proposed state from a proposal distribution, then using an acceptance rule to decide whether to accept the proposal or stay at the current state (Robert and Casella, 1999).