We study the Bayesian solution of a linear inverse problem in a separable Hilbert space setting with Gaussian prior and noise distribution. Our contribution is to propose a new Bayes estimator which is a linear and continuous estimator on the whole space and is stronger than the mean of the exact Gaussian posterior distribution which is only defined as a measurable linear transformation. Our estimator is the mean of a slightly modified posterior distribution called regularized posterior distribution. Frequentist consistency of our estimator and of the regularized posterior distribution is proved. A Monte Carlo study and an application to real data confirm good small-sample properties of our procedure.
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Titolo: | Regularized Posteriors in Linear ill-Posed Inverse Problems |
Data di pubblicazione: | 2012 |
Autori: | |
Autori: | J. P., Florens; Simoni, Anna |
Rivista: | SCANDINAVIAN JOURNAL OF STATISTICS |
Abstract: | We study the Bayesian solution of a linear inverse problem in a separable Hilbert space setting with Gaussian prior and noise distribution. Our contribution is to propose a new Bayes estimator which is a linear and continuous estimator on the whole space and is stronger than the mean of the exact Gaussian posterior distribution which is only defined as a measurable linear transformation. Our estimator is the mean of a slightly modified posterior distribution called regularized posterior distribution. Frequentist consistency of our estimator and of the regularized posterior distribution is proved. A Monte Carlo study and an application to real data confirm good small-sample properties of our procedure. |
Codice identificativo Scopus: | 2-s2.0-84860995589 |
Codice identificativo ISI: | WOS:000304000600005 |
Appare nelle tipologie: | 01 - Article in academic journal / Articolo su rivista Scientifica |