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Estimating Anomalies from Indirect Observations

✍ Scribed by Jari P. Kaipio; Erkki Somersalo

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
340 KB
Volume
181
Category
Article
ISSN
0021-9991

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✦ Synopsis

Indirect observations often lead to ill-posed inverse problems, where the use of prior information plays a crucial role. When correctly used, informative priors should be based on our belief of what the typical situation looks like, while the aim of the measurement procedure is often to find deviations from the typical. This work proposes a method of implementing priors that on one hand reflects the belief concerning the typical situation and on the other retains sensitivity to anomalies of the prescribed type. Numerical results are based on Bayesian sampling methods.

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## Abstract Let __X__~1~, … , __X__~n~, be a collection of iid discrete random variables, and __Y__~1~, … , __Y__~m~, a set of noisy observations of such variables. Assume each observation Y~a~, to be a random function of a random subset of the __X__~i~,s, and consider the conditional distribution