dorsal/arxiv
View SchemaThe incomplete beta function law for parallel tempering sampling of classical canonical systems
| Authors | Cristian Predescu, Mihaela Predescu, Cristian V. Ciobanu |
|---|---|
| Categories | |
| ArXiv ID | physics/0310101 |
| URL | https://arxiv.org/abs/physics/0310101 |
| DOI | 10.1063/1.1644093 |
| Journal | J. Chem. Phys. 120, 4119 (2004). |
Abstract
We show that the acceptance probability for swaps in the parallel tempering Monte Carlo method for classical canonical systems is given by a universal function that depends on the average statistical fluctuations of the potential and on the ratio of the temperatures. The law, called the incomplete beta function law, is valid in the limit that the two temperatures involved in swaps are close to one another. An empirical version of the law, which involves the heat capacity of the system, is developed and tested on a Lennard-Jones cluster. We argue that the best initial guess for the distribution of intermediate temperatures for parallel tempering is a geometric progression and we also propose a technique for the computation of optimal temperature schedules. Finally, we demonstrate that the swap efficiency of the parallel tempering method for condensed-phase systems decreases naturally to zero at least as fast as the inverse square root of the dimensionality of the physical system.
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"abstract": "We show that the acceptance probability for swaps in the parallel tempering\nMonte Carlo method for classical canonical systems is given by a universal\nfunction that depends on the average statistical fluctuations of the potential\nand on the ratio of the temperatures. The law, called the incomplete beta\nfunction law, is valid in the limit that the two temperatures involved in swaps\nare close to one another. An empirical version of the law, which involves the\nheat capacity of the system, is developed and tested on a Lennard-Jones\ncluster. We argue that the best initial guess for the distribution of\nintermediate temperatures for parallel tempering is a geometric progression and\nwe also propose a technique for the computation of optimal temperature\nschedules. Finally, we demonstrate that the swap efficiency of the parallel\ntempering method for condensed-phase systems decreases naturally to zero at\nleast as fast as the inverse square root of the dimensionality of the physical\nsystem.",
"arxiv_id": "physics/0310101",
"authors": [
"Cristian Predescu",
"Mihaela Predescu",
"Cristian V. Ciobanu"
],
"categories": [
"physics.chem-ph",
"physics.comp-ph"
],
"doi": "10.1063/1.1644093",
"journal_ref": "J. Chem. Phys. 120, 4119 (2004).",
"title": "The incomplete beta function law for parallel tempering sampling of classical canonical systems",
"url": "https://arxiv.org/abs/physics/0310101"
},
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