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Article

Automatic Tempered Posterior Distributions for Bayesian Inversion Problems

1
Department of Signal Processing, Universidad rey Juan Carlos (URJC), 28942 Madrid, Spain
2
Department of Statistics, Universidad Carlos III de Madrid (UC3M), 28911 Madrid, Spain
3
Department of Signal Processing, Universidad Carlos III de Madrid (UC3M), 28911 Madrid, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Daniel-Ioan Curiac
Mathematics 2021, 9(7), 784; https://doi.org/10.3390/math9070784
Received: 27 February 2021 / Revised: 26 March 2021 / Accepted: 1 April 2021 / Published: 6 April 2021
(This article belongs to the Special Issue Recent Advances in Data Science)
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 are carried out using distinct (but interacting) methods. 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 with 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 current estimate of the noise power. A complete Bayesian study over the model parameters and the scale parameter can also be performed. Numerical experiments show the benefits of the proposed approach. View Full-Text
Keywords: Bayesian inference; importance sampling; MCMC; inversion problems Bayesian inference; importance sampling; MCMC; inversion problems
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MDPI and ACS Style

Martino, L.; Llorente, F.; Curbelo, E.; López-Santiago, J.; Míguez, J. Automatic Tempered Posterior Distributions for Bayesian Inversion Problems. Mathematics 2021, 9, 784. https://doi.org/10.3390/math9070784

AMA Style

Martino L, Llorente F, Curbelo E, López-Santiago J, Míguez J. Automatic Tempered Posterior Distributions for Bayesian Inversion Problems. Mathematics. 2021; 9(7):784. https://doi.org/10.3390/math9070784

Chicago/Turabian Style

Martino, Luca, Fernando Llorente, Ernesto Curbelo, Javier López-Santiago, and Joaquín Míguez. 2021. "Automatic Tempered Posterior Distributions for Bayesian Inversion Problems" Mathematics 9, no. 7: 784. https://doi.org/10.3390/math9070784

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