ENBIS-16 in Sheffield

11 – 15 September 2016; Sheffield Abstract submission: 20 March – 4 July 2016

Well-Posedness Conditions in Stochastic Inversion Problems

13 September 2016, 12:40 – 13:10

Abstract

Submitted by
Nicolas Bousquet
Authors
Nicolas Bousquet (EDF R&D), Mélanie Blazère (EDF R&D and IMT)
Abstract
We consider a stochastic inversion problem defined by the knowledge of observations which are assumed to be realizations of a random variable Y* such that Y* = Y + u, and Y = g(X), where X is a random Gaussian vector with unknown parameters and u is an (experimental or/and process) noise with known distribution fu, and g is some deterministic function (possibly a black-box computer model). This inversion problem can be solved in frequentist or Bayesian frameworks (possibly by linearizing g), using missing data algorithms. To be solved it requires that several conditions of well-posedness and identifiability are gathered. One of them is adressed in this talk, which arises from predicted sensivity analysis. Imagine that the problem is solved. Any sensitivity study should highlight that the main source of uncertainty, explaining the variations of Y*, is X and not u. In practice, this diagnostic is established a posteriori, as a check for an estimated solution. However, it is more than desirable that this applies as a calibration constraint. This talk will propose a new general rule in the case when g is linearizable, based on Fisher information, and makes strong links with Sobol' indices. The approach is tested over toy examples and a hydraulical example, and compared with usual stochastic inversion methodologies that do not consider this well-posedness condition a priori.

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