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Download the Paper (889 K, PDF file) - January 9, 2008 Tell a colleague about it. Printing Tips: Select 'print as image' in the Acrobat print dialog if you have trouble printing.

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.

SUGGESTED CITATION:
Qing Zhou and Wing H. Wong, "Reconstructing the Energy Landscape of a Distribution from Monte Carlo Samples" (January 9, 2008). Department of Statistics, UCLA. Department of Statistics Papers. Paper 2008010907.
http://repositories.cdlib.org/uclastat/papers/2008010907