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Title: ADAPTIVE ANNEALED IMPORTANCE SAMPLING FOR MULTIMODAL POSTERIOR EXPLORATION AND MODEL SELECTION WITH APPLICATION TO EXTRASOLAR PLANET DETECTION

We describe an algorithm that can adaptively provide mixture summaries of multimodal posterior distributions. The parameter space of the involved posteriors ranges in size from a few dimensions to dozens of dimensions. This work was motivated by an astrophysical problem called extrasolar planet (exoplanet) detection, wherein the computation of stochastic integrals that are required for Bayesian model comparison is challenging. The difficulty comes from the highly nonlinear models that lead to multimodal posterior distributions. We resort to importance sampling (IS) to estimate the integrals, and thus translate the problem to be how to find a parametric approximation of the posterior. To capture the multimodal structure in the posterior, we initialize a mixture proposal distribution and then tailor its parameters elaborately to make it resemble the posterior to the greatest extent possible. We use the effective sample size (ESS) calculated based on the IS draws to measure the degree of approximation. The bigger the ESS is, the better the proposal resembles the posterior. A difficulty within this tailoring operation lies in the adjustment of the number of mixing components in the mixture proposal. Brute force methods just preset it as a large constant, which leads to an increase in the requiredmore » computational resources. We provide an iterative delete/merge/add process, which works in tandem with an expectation-maximization step to tailor such a number online. The efficiency of our proposed method is tested via both simulation studies and real exoplanet data analysis.« less
Authors:
 [1]
  1. School of Computer Science and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210023 (China)
Publication Date:
OSTI Identifier:
22340194
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal, Supplement Series; Journal Volume: 213; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALGORITHMS; ASTROPHYSICS; DATA ANALYSIS; DETECTION; INTEGRALS; ITERATIVE METHODS; MATHEMATICAL SPACE; NONLINEAR PROBLEMS; PLANETS; SAMPLING; SIMULATION; STARS; STOCHASTIC PROCESSES