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Automatic tempered posterior distributions for bayesian inversion problems

Mathematics, ISSN: 2227-7390, Vol: 9, Issue: 7
2021
  • 10
    Citations
  • 0
    Usage
  • 0
    Captures
  • 1
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    10
    • Citation Indexes
      10
  • Mentions
    1
    • Blog Mentions
      1
      • Blog
        1

Article Description

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.

Bibliographic Details

Luca Martino; Javier López-Santiago; Joaquín Míguez; Fernando Llorente; Ernesto Cuberlo

MDPI AG

Computer Science; Mathematics; Engineering

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