Reconstructing the energy landscape of a distribution from Monte Carlo samples

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dc.creatorZhou, Qing
dc.creatorWong, Wing Hung
dc.date2009-01-26
dc.date.accessioned2026-07-07T12:34:33Z
dc.date.available2026-07-07T12:34:33Z
dc.descriptionDefining the energy function as the negative logarithm of the density, we explore the energy landscape of a distribution via the tree of sublevel sets of its energy. This tree represents the hierarchy among the connected components of the sublevel sets. We propose ways to annotate the tree so that it provides information on both topological and statistical aspects of the distribution, such as the local energy minima (local modes), their local domains and volumes, and the barriers between them. We develop a computational method to estimate the tree and reconstruct the energy landscape from Monte Carlo samples simulated at a wide energy range of a distribution. This method can be applied to any arbitrary distribution on a space with defined connectedness. We test the method on multimodal distributions and posterior distributions to show that our estimated trees are accurate compared to theoretical values. When used to perform Bayesian inference of DNA sequence segmentation, this approach reveals much more information than the standard approach based on marginal posterior distributions.
dc.descriptionPublished in at http://dx.doi.org/10.1214/08-AOAS196 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0901.3999
dc.identifierhttp://arxiv.org/abs/0901.3999
dc.identifierAnnals of Applied Statistics 2008, Vol. 2, No. 4, 1307-1331
dc.identifierdoi:10.1214/08-AOAS196
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217473
dc.subjectApplications
dc.titleReconstructing the energy landscape of a distribution from Monte Carlo samples
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