Working Paper Article Version 1 This version is not peer-reviewed

Automatic Tempered Posterior Distributions for Bayesian Inversion Problems

Version 1 : Received: 27 February 2021 / Approved: 1 March 2021 / Online: 1 March 2021 (14:04:15 CET)

A peer-reviewed article of this Preprint also exists.

Martino, L.; Llorente, F.; Cuberlo, E.; López-Santiago, J.; Míguez, J. Automatic Tempered Posterior Distributions for Bayesian Inversion Problems. Mathematics 2021, 9, 784. Martino, L.; Llorente, F.; Cuberlo, E.; López-Santiago, J.; Míguez, J. Automatic Tempered Posterior Distributions for Bayesian Inversion Problems. Mathematics 2021, 9, 784.

Journal reference: Mathematics 2021, 9, 784
DOI: 10.3390/math9070784

Abstract

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the variables of interest (i.e., the parameters of the model to invert), whereas we employ a maximum likelihood approach for the estimation of the noise power. The whole technique is implemented by means of an iterative procedure, alternating sampling and optimization steps. Moreover, the noise power is also used as a tempered parameter for the posterior distribution of the the variables of interest. Therefore, a sequence of tempered posterior densities is generated, where the tempered parameter is automatically selected according to the actual estimation of the noise power. A complete Bayesian study over the model parameters and the scale parameter can be also performed. Numerical experiments show the benefits of the proposed approach.

Subject Areas

Bayesian Inference; Importance Sampling; Inversion Problems; Exoplanets

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