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Markov chain Monte Carlo (MCMC) algorithms are widely used to sample fromcomplicated distributions, especially to sample from the posterior distributionin Bayesian inference. However, MCMC is not directly applicable when facing thedoubly intractable problem. In this paper, we discussed and compared twoexisting solutions -- Pseudo-marginal Monte Carlo and Exchange Algorithm. Thispaper also proposes a novel algorithm: Multi-armed Bandit MCMC (MABMC), whichchooses between two (or more) randomized acceptance ratios in each step. MABMCcould be applied directly to incorporate Pseudo-marginal Monte Carlo andExchange algorithm, with higher average acceptance probability.

A Multi-armed Bandit MCMC, with applications in sampling from doubly intractable posterior