Canonical transition probabilities for adaptive Metropolis simulation

Abstract

We examine non-Boltzmann Monte Carlo algorithms used to study slowly relaxing systems. By adding a simple bookkeeping step to the Metropolis algorithm, we obtain statistical estimators of canonical macrostate probabilities. These estimators enable a natural accumulation of statistics from simulations having different importance weights, enable temperature extrapolation without using energy to define macrostate labels, improve parallelization, and reduce variance. We illustrate with an Ising model example.