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