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2013 Bayesian inverse problems with non-conjugate priors
Kolyan Ray
Electron. J. Statist. 7: 2516-2549 (2013). DOI: 10.1214/13-EJS851

Abstract

We investigate the frequentist posterior contraction rate of nonparametric Bayesian procedures in linear inverse problems in both the mildly and severely ill-posed cases. A theorem is proved in a general Hilbert space setting under approximation-theoretic assumptions on the prior. The result is applied to non-conjugate priors, notably sieve and wavelet series priors, as well as in the conjugate setting. In the mildly ill-posed setting minimax optimal rates are obtained, with sieve priors being rate adaptive over Sobolev classes. In the severely ill-posed setting, oversmoothing the prior yields minimax rates. Previously established results in the conjugate setting are obtained using this method. Examples of applications include deconvolution, recovering the initial condition in the heat equation and the Radon transform.

Citation

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Kolyan Ray. "Bayesian inverse problems with non-conjugate priors." Electron. J. Statist. 7 2516 - 2549, 2013. https://doi.org/10.1214/13-EJS851

Information

Published: 2013
First available in Project Euclid: 8 October 2013

zbMATH: 1294.62107
MathSciNet: MR3117105
Digital Object Identifier: 10.1214/13-EJS851

Subjects:
Primary: 62G20
Secondary: 62G05, 62G08

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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