Automatic Tempered Posterior Distributions for Bayesian Inversion Problems

Luca Martino, Fernando Llorente, Ernesto Curbelo, Javier López-Santiago and Joaquín Míguez
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Luca Martino: Department of Signal Processing, Universidad rey Juan Carlos (URJC), 28942 Madrid, Spain
Fernando Llorente: Department of Statistics, Universidad Carlos III de Madrid (UC3M), 28911 Madrid, Spain
Ernesto Curbelo: Department of Statistics, Universidad Carlos III de Madrid (UC3M), 28911 Madrid, Spain
Javier López-Santiago: Department of Signal Processing, Universidad Carlos III de Madrid (UC3M), 28911 Madrid, Spain
Joaquín Míguez: Department of Signal Processing, Universidad Carlos III de Madrid (UC3M), 28911 Madrid, Spain

Mathematics, 2021, vol. 9, issue 7, 1-17

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 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.

Keywords: Bayesian inference; importance sampling; MCMC; inversion problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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