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Title: Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems

Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. One can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior.
Authors:
 [1] ;  [2] ;  [1] ;  [2] ;  [3] ;  [1] ;  [2]
  1. Lawrence Berkeley National Laboratory (United States)
  2. (United States)
  3. Department of Mathematics, University of Kansas (United States)
Publication Date:
OSTI Identifier:
22382181
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 282; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; CHAOS THEORY; COMPARATIVE EVALUATIONS; INVERSE SCATTERING PROBLEM; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; POLYNOMIALS