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A Full Bayesian Approach for Inverse Problems

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Maximum Entropy and Bayesian Methods

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 79))

Abstract

The main object of this paper is to present some general concepts of Bayesian inference and more specifically the estimation of the hyperparameters in inverse problems. We consider a general linear situation where we are given some data y related to the unknown parameters z by y = Az + n and where we can assign the probability laws p(x|θ), p(y|x,ß), p(ß) and p(θ). The main discussion is then how to infer x,θ and | either individually or any combinations of them. Different situations are considered and discussed. As an important example, we consider the case where θ and | are the precision parameters of the Gaussian laws to whom we assign Gamma priors and we propose some new and practical algorithms to estimate them simultaneously. Comparisons and links with other classical methods such as maximum likelihood are presented.

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Author information

Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes (CNRS-ESE-UPS), Supélec, Plateau de Moulon, 91192, Gif-sur-Yvette, France

    Ali Mohammad-Djafari

Authors
  1. Ali Mohammad-Djafari
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Editor information

Editors and Affiliations

  1. Dynamic Experimentation Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA

    Kenneth M. Hanson

  2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA

    Richard N. Silver

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© 1996 Springer Science+Business Media Dordrecht

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Mohammad-Djafari, A. (1996). A Full Bayesian Approach for Inverse Problems. In: Hanson, K.M., Silver, R.N. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5430-7_16

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  • DOI: https://doi.org/10.1007/978-94-011-5430-7_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6284-8

  • Online ISBN: 978-94-011-5430-7

  • eBook Packages: Springer Book Archive

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