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Erschienen in:
Introduction Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

6. Bayesian Inverse Problems

verfasst von : T. J. Sullivan

Erschienen in: Introduction to Uncertainty Quantification

Verlag: Springer International Publishing

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Abstract

This chapter provides a general introduction, at the high level, to the backward propagation of uncertainty/information in the solution of inverse problems, and specifically a Bayesian probabilistic perspective on such inverse problems. Under the umbrella of inverse problems, we consider parameter estimation and regression. One specific aim is to make clear the connection between regularization and the application of a Bayesian prior. The filtering methods of Chapter 7 fall under the general umbrella of Bayesian approaches to inverse problems, but have an additional emphasis on real-time computational expediency.

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Vorheriges Kapitel Measures of Information and Uncertainty
Nächstes Kapitel Filtering and Data Assimilation
Fußnoten
1
Take a moment to reconcile the statement “there may exist minimizing sequences that do not have a limit in \( \mathcal{U} \)” with \( \mathcal{U} \) being a Banach space.
 
2
Here, the minimization is meant in the sense of positive semi-definite operators: for two operators A and B, we say that A ≤ B if B − A is a positive semi-definite operator.
 
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Metadaten
Titel
Bayesian Inverse Problems
verfasst von
T. J. Sullivan
Copyright-Jahr
2015
Buch
Introduction to Uncertainty Quantification

Print ISBN: 978-3-319-23394-9

Electronic ISBN: 978-3-319-23395-6

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-23395-6_6