Optimized replica gas estimation of absolute integrals and partition functions.

Journal Article · Fri Jan 01 00:00:00 EST 2010 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PhysRevE.82.031132· OSTI ID:1039135

Minh, D ^[1]

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1. Biosciences Division

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.

• Research Organization: Argonne National Lab. (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: DE-AC02-06CH11357
• OSTI ID: 1039135
• Report Number(s): ANL/BIO/JA-66160; TRN: US201209%%197
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 82, Issue 3; ISSN 1539-3755
• Country of Publication: United States
• Language: ENGLISH

Related Subjects

36 MATERIALS SCIENCE
ALGORITHMS
CONVERGENCE
FUNCTIONALS
ISING MODEL
PARTITION FUNCTIONS
REPLICAS
WEIGHTING FUNCTIONS