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Activity Number:
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399
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2008 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #302232 |
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Title:
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Geometric Ergodicity of Hybrid Samplers for Ill-Posed Inverse Problems
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Author(s):
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Radu Herbei*+ and Ian W. McKeague
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Companies:
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The Ohio State University and Columbia University
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Address:
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1958 Neil Ave, Cockins Hall, Columbus, OH, 43210,
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Keywords:
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hybrid samplers ; geometric ergodicity ; MCMC ; PDE
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Abstract:
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Ill-posed inverse problems arise in many scientific fields, and statistical methods to address such problems have been studied extensively. In the Bayesian approach to inverse problems, regularization is imposed by specifying a prior distribution on the parameters of interest and MCMC samplers are used to extract information about its posterior distribution. The aim of the present paper is to investigate the convergence properties of the random-scan random walk Metropolis (RSM) algorithm, which is known to converge geometrically under certain conditions. We provide an accessible set of sufficient conditions, in terms of the observational model and the prior, to ensure geometric ergodicity of RSM samplers of the posterior distribution. We illustrate how these conditions can be easily checked in the context of an application to the inversion of oceanographic tracer data.
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