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Abstract: In contrast with most Monte Carlo integration algorithms, which are used toestimate ratios, the replica gas identities recently introduced by Adib enablethe estimation of absolute integrals and partition functions using multiplecopies of a system and normalized transition functions. Here, an optimized formis presented. After generalizing a replica gas identity with an arbitraryweighting function, we obtain a functional form that has the minimal asymptoticvariance for samples from two replicas and is provably good for a largernumber. This equation is demonstrated to improve the convergence of partitionfunction estimates in a 2D Ising model.



Author: David D. L. Minh

Source: https://arxiv.org/







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