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December 2008 Reconstructing the energy landscape of a distribution from Monte Carlo samples
Qing Zhou, Wing Hung Wong
Ann. Appl. Stat. 2(4): 1307-1331 (December 2008). DOI: 10.1214/08-AOAS196

Abstract

Defining 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.

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Qing Zhou. Wing Hung Wong. "Reconstructing the energy landscape of a distribution from Monte Carlo samples." Ann. Appl. Stat. 2 (4) 1307 - 1331, December 2008. https://doi.org/10.1214/08-AOAS196

Information

Published: December 2008
First available in Project Euclid: 8 January 2009

zbMATH: 1169.62008
MathSciNet: MR2655661
Digital Object Identifier: 10.1214/08-AOAS196

Keywords: change point , cluster tree , connected component , disconnectivity graph , Monte Carlo , posterior distribution , sequence segmentation , sublevel set

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.2 • No. 4 • December 2008
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