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 twodimensional Ising model.
 Authors:

 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/JA66160
Journal ID: ISSN 15393755; TRN: US201209%%197
 DOE Contract Number:
 DEAC0206CH11357
 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 15393755
 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 twodimensional Ising model.},
doi = {10.1103/PhysRevE.82.031132},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},
issn = {15393755},
number = 3,
volume = 82,
place = {United States},
year = {2010},
month = {1}
}
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