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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 427203, 12 pages
http://dx.doi.org/10.1155/2014/427203
Research Article

Effective Parameter Dimension via Bayesian Model Selection in the Inverse Acoustic Scattering Problem

CIMAT A.C, Jalisco S/N, Valenciana, 36240 México, GTO, Mexico

Received 8 April 2014; Revised 23 July 2014; Accepted 23 July 2014; Published 7 September 2014

Academic Editor: Fatih Yaman

Copyright © 2014 Abel Palafox et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We address a prototype inverse scattering problem in the interface of applied mathematics, statistics, and scientific computing. We pose the acoustic inverse scattering problem in a Bayesian inference perspective and simulate from the posterior distribution using MCMC. The PDE forward map is implemented using high performance computing methods. We implement a standard Bayesian model selection method to estimate an effective number of Fourier coefficients that may be retrieved from noisy data within a standard formulation.