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EnglishWe 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. | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1111/j.1467-9469.2011.00784.x | |
| Appare nelle tipologie: | 01 - Article in academic journal / Articolo su rivista scientifica |
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http://hdl.handle.net/11565/3731855
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