dorsal/arxiv
View SchemaPerfect Tempering
| Authors | M. Daghofer, M. Konegger, H. G. Evertz, W. von der Linden |
|---|---|
| Categories | |
| ArXiv ID | physics/0512167 |
| URL | https://arxiv.org/abs/physics/0512167 |
| DOI | 10.1063/1.1835233 |
| Journal | AIP Conf. Proc. vol. 735 (2004), pages 355-362 |
Abstract
Multimodal structures in the sampling density (e.g. two competing phases) can be a serious problem for traditional Markov Chain Monte Carlo (MCMC), because correct sampling of the different structures can only be guaranteed for infinite sampling time. Samples may not decouple from the initial configuration for a long time and autocorrelation times may be hard to determine. We analyze a suitable modification (C. J. Geyer and E. A. Thompson, J. Amer. Statist. Assoc., 90, 909, 1995) of the simulated tempering idea (E. Marinari and G. Parisi, Europhys. Lett. 19, 451, 1992), which has orders of magnitude smaller autocorrelation times for multimodal sampling densities and which samples all peaks of multimodal structures according to their weight. The method generates exact, i.e. uncorrelated, samples and thus gives access to reliable error estimates. Exact tempering is applicable to arbitrary (continuous or discreet) sampling densities and moreover presents a possibility to calculate integrals over the density (e.g. the partition function for the Boltzmann distribution), which are not accessible by usual MCMC.
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"abstract": "Multimodal structures in the sampling density (e.g. two competing phases) can\nbe a serious problem for traditional Markov Chain Monte Carlo (MCMC), because\ncorrect sampling of the different structures can only be guaranteed for\ninfinite sampling time. Samples may not decouple from the initial configuration\nfor a long time and autocorrelation times may be hard to determine.\n We analyze a suitable modification (C. J. Geyer and E. A. Thompson, J. Amer.\nStatist. Assoc., 90, 909, 1995) of the simulated tempering idea (E. Marinari\nand G. Parisi, Europhys. Lett. 19, 451, 1992), which has orders of magnitude\nsmaller autocorrelation times for multimodal sampling densities and which\nsamples all peaks of multimodal structures according to their weight. The\nmethod generates exact, i.e. uncorrelated, samples and thus gives access to\nreliable error estimates. Exact tempering is applicable to arbitrary\n(continuous or discreet) sampling densities and moreover presents a possibility\nto calculate integrals over the density (e.g. the partition function for the\nBoltzmann distribution), which are not accessible by usual MCMC.",
"arxiv_id": "physics/0512167",
"authors": [
"M. Daghofer",
"M. Konegger",
"H. G. Evertz",
"W. von der Linden"
],
"categories": [
"physics.data-an",
"cond-mat.other",
"physics.comp-ph"
],
"doi": "10.1063/1.1835233",
"journal_ref": "AIP Conf. Proc. vol. 735 (2004), pages 355-362",
"title": "Perfect Tempering",
"url": "https://arxiv.org/abs/physics/0512167"
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