Open Access
February 1997 Bayesian methods and maximum entropy for ill-posed inverse problems
F. Gamboa, E. Gassiat
Ann. Statist. 25(1): 328-350 (February 1997). DOI: 10.1214/aos/1034276632


In this paper, we study linear inverse problems where some generalized moments of an unknown positive measure are observed. We introduce a new construction, called the maximum entropy on the mean method (MEM), which relies on a suitable sequence of finite-dimensional discretized inverse problems. Its advantage is threefold: It allows us to interpret all usual deterministic methods as Bayesian methods; it gives a very convenient way of taking into account prior information; it also leads to new criteria for the existence question concerning the linear inverse problem which will be a starting point for the investigation of superresolution phenomena. The key tool in this work is the large deviations property of some discrete random measure connected with the reconstruction procedure.


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F. Gamboa. E. Gassiat. "Bayesian methods and maximum entropy for ill-posed inverse problems." Ann. Statist. 25 (1) 328 - 350, February 1997.


Published: February 1997
First available in Project Euclid: 10 October 2002

zbMATH: 0871.62010
MathSciNet: MR1429928
Digital Object Identifier: 10.1214/aos/1034276632

Primary: 60A99 , 62A99

Keywords: Bayesian statistics , large deviations , Moment problems

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.25 • No. 1 • February 1997
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