A Multi-armed Bandit MCMC, with applications in sampling from doubly intractable posterior
This addresses a specific bottleneck in MCMC methods for Bayesian inference, offering an incremental improvement for researchers and practitioners dealing with complex statistical models.
The paper tackles the problem of sampling from doubly intractable posterior distributions in Bayesian inference by proposing a novel Multi-armed Bandit MCMC (MABMC) algorithm, which achieves higher average acceptance probability compared to existing methods like Pseudo-marginal Monte Carlo and Exchange Algorithm.
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.