Analysis of Exchange Ratio for Exchange Monte Carlo Method

The exchange Monte Carlo method was proposed as an improved algorithm of Markov Chain Monte Carlo method and its effectiveness has been shown in many fields. In the exchange Monte Carlo method, the setting of temperatures is important to make the algorithm efficient because this setting controls the exchange ratio, with which the position exchange between two sequences is accepted. However, the mathematical foundation of exchange MC method has not yet been established. In this paper, we rigorously prove the mathematical relation between the symmetrized Kullback divergence and the exchange ratio, by which the optimal setting of temperatures is devised.