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2022 Designing truncated priors for direct and inverse Bayesian problems
Sergios Agapiou, Peter Mathé
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Electron. J. Statist. 16(1): 158-200 (2022). DOI: 10.1214/21-EJS1966

Abstract

The Bayesian approach to inverse problems with functional unknowns, has received significant attention in recent years. An important component of the developing theory is the study of the asymptotic performance of the posterior distribution in the frequentist setting. The present paper contributes to the area of Bayesian inverse problems by formulating a posterior contraction theory for linear inverse problems, with truncated Gaussian series priors, and under general smoothness assumptions. Emphasis is on the intrinsic role of the truncation point both for the direct as well as for the inverse problem, which are related through the modulus of continuity as this was recently highlighted by Knapik and Salomond (2018).

Acknowledgments

The authors are thankful to an anonymous associate editor and two anonymous referees, for constructive comments which led to a substantially improved presentation of the results.

Citation

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Sergios Agapiou. Peter Mathé. "Designing truncated priors for direct and inverse Bayesian problems." Electron. J. Statist. 16 (1) 158 - 200, 2022. https://doi.org/10.1214/21-EJS1966

Information

Received: 1 May 2021; Published: 2022
First available in Project Euclid: 6 January 2022

Digital Object Identifier: 10.1214/21-EJS1966

Subjects:
Primary: 62G20
Secondary: 45Q05, 62C10, 62F15

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Vol.16 • No. 1 • 2022
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