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Title: Optimized replica gas estimation of absolute integrals and partition functions.

Abstract

In contrast with most Monte Carlo integration algorithms, which are used to estimate ratios, the replica gas identities recently introduced by Adib enable the estimation of absolute integrals and partition functions using multiple copies of a system and normalized transition functions. Here, an optimized form is presented. After generalizing a replica gas identity with an arbitrary weighting function, we obtain a functional form that has the minimal asymptotic variance for samples from two replicas and is provably good for a larger number. This equation is demonstrated to improve the convergence of partition function estimates in a two-dimensional Ising model.

Authors:
 [1]
  1. Biosciences Division
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1039135
Report Number(s):
ANL/BIO/JA-66160
Journal ID: ISSN 1539-3755; TRN: US201209%%197
DOE Contract Number:  
DE-AC02-06CH11357
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)
Additional Journal Information:
Journal Volume: 82; Journal Issue: 3; Journal ID: ISSN 1539-3755
Country of Publication:
United States
Language:
ENGLISH
Subject:
36 MATERIALS SCIENCE; ALGORITHMS; CONVERGENCE; FUNCTIONALS; ISING MODEL; PARTITION FUNCTIONS; REPLICAS; WEIGHTING FUNCTIONS

Citation Formats

Minh, D. Optimized replica gas estimation of absolute integrals and partition functions.. United States: N. p., 2010. Web. doi:10.1103/PhysRevE.82.031132.
Minh, D. Optimized replica gas estimation of absolute integrals and partition functions.. United States. doi:10.1103/PhysRevE.82.031132.
Minh, D. Fri . "Optimized replica gas estimation of absolute integrals and partition functions.". United States. doi:10.1103/PhysRevE.82.031132.
@article{osti_1039135,
title = {Optimized replica gas estimation of absolute integrals and partition functions.},
author = {Minh, D},
abstractNote = {In contrast with most Monte Carlo integration algorithms, which are used to estimate ratios, the replica gas identities recently introduced by Adib enable the estimation of absolute integrals and partition functions using multiple copies of a system and normalized transition functions. Here, an optimized form is presented. After generalizing a replica gas identity with an arbitrary weighting function, we obtain a functional form that has the minimal asymptotic variance for samples from two replicas and is provably good for a larger number. This equation is demonstrated to improve the convergence of partition function estimates in a two-dimensional Ising model.},
doi = {10.1103/PhysRevE.82.031132},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},
issn = {1539-3755},
number = 3,
volume = 82,
place = {United States},
year = {2010},
month = {1}
}