Sequential Exchange Monte Carlo: Sampling Method for Multimodal Distribution without Parameter Tuning

Abstract: The Replica Exchange Monte Carlo (REMC) method, a Markov Chain Monte Carlo (MCMC) algorithm for sampling multimodal distributions, is typically employed in Bayesian inference for complex models. Using the REMC method, multiple probability distributions with different temperatures are defined to enhance sampling efficiency and allow for the high-precision computation of Bayesian free energy. However, the REMC method requires the tuning of many parameters, including the number of distributions, temperature, and step size, which makes it difficult for nonexperts to effectively use. Thus, we propose the Sequential Exchange Monte Carlo (SEMC) method, which automates the tuning of parameters by sequentially determining the temperature and step size. Numerical experiments showed that SEMC is as efficient as parameter-tuned REMC and parameter-tuned Sequential Monte Carlo Samplers (SMCS), which is also effective for the Bayesian inference of complex models.