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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2014011073
pages 73-98

BAYESIAN INFERENCE FOR INVERSE PROBLEMS OCCURRING IN UNCERTAINTY ANALYSIS

Shuai Fu
University Paris-Sud 11, France; EDF, R&D, France
Gilles Celeux
Inria Saclay-Ile-de-France
Nicolas Bousquet
EDF, R&D, France
Mathieu Couplet
EDF, R&D, France

ABSTRACT

The inverse problem considered here is the estimation of the distribution of a nonobserved random variable X, linked through a time-consuming physical model H to some noisy observed data Y. Bayesian inference is considered to account for prior expert knowledge on X in a small sample size setting. A Metropolis-Hastings-within-Gibbs algorithm is used to compute the posterior distribution of the parameters of the distribution of X through a data augmentation process. Since running H is quite expensive, this inference is achieved by a kriging emulator interpolating H from a numerical design of experiments (DOE). This approach involves several errors of different natures and, in this article, we pay effort to measure and reduce the possible impact of those errors. In particular, we propose to use the so-called DAC criterion to assess in the same exercise the relevance of the DOE and the prior distribution. After describing the calculation of this criterion for the emulator at hand, its behavior is illustrated on numerical experiments.