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Bayesian Theory and Applications$
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Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens

Print publication date: 2013

Print ISBN-13: 9780199695607

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199695607.001.0001

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Approximate marginalization over modelling errors and uncertainties in inverse problems

Approximate marginalization over modelling errors and uncertainties in inverse problems

Chapter:
(p.644) 32 Approximate marginalization over modelling errors and uncertainties in inverse problems
Source:
Bayesian Theory and Applications
Author(s):

Jari Kaipio

Ville Kolehmainen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199695607.003.0032

This chapter discusses the so-called approximation error approach, which was originally meant to model numerical model reduction only. The approach is based on a number of consecutive approximations for the associated models and densities, based on Bayesian modelling of all uncertainties, approximations, and unknowns. The goal is to obtain highly approximate ‘dirty but fast’ computational models, which are feasible in the sense that the actual unknowns should lie within a couple of approximate credibility intervals. The approach is shown to be feasible for a number of modelling errors and uncertainties, including drastic model reduction, unknown geometry and boundary conditions, and highly approximate physical models. The approach also provides feasible spread estimates, thus enabling, for example, optimal stochastic (feedback) control.

Keywords:   Bayesian modelling, modelling errors, likelihood model, approximation error approach

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