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Activity Number:
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219
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Type:
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Contributed
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Date/Time:
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Monday, August 3, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #303511 |
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Title:
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Reconstructing the Energy Landscape of a Distribution from Monte Carlo Samples
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Author(s):
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Qing Zhou*+ and Wing H. Wong
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Companies:
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University of California, Los Angeles and Stanford University
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Address:
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Department of Statistics, 8125 Math Sciences Bldg., Los Angeles, CA, 90024,
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Keywords:
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Monte Carlo ; sublevel set ; connected component ; posterior distribution ; cluster tree ; disconnectivity graph
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Abstract:
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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 sublevel sets. We propose ways to annotate the tree so that it provides information in both topological and statistical aspects of the distribution, such as the local energy minima, their local domains and volumes, and the barriers between them. We develop a computational method to estimate the tree 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. 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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