Automatic Tempered Posterior Distributions for Bayesian Inversion Problems
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 in...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/7/784 |
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| author | Luca Martino Fernando Llorente Ernesto Curbelo Javier López-Santiago Joaquín Míguez |
| author_facet | Luca Martino Fernando Llorente Ernesto Curbelo Javier López-Santiago Joaquín Míguez |
| author_sort | Luca Martino |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T12:36:16Z |
| format | Article |
| id | doaj.art-ef6da7b9362d428ea680690301bfe504 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T12:36:16Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ef6da7b9362d428ea680690301bfe5042023-11-21T14:18:26ZengMDPI AGMathematics2227-73902021-04-019778410.3390/math9070784Automatic Tempered Posterior Distributions for Bayesian Inversion ProblemsLuca Martino0Fernando Llorente1Ernesto Curbelo2Javier López-Santiago3Joaquín Míguez4Department of Signal Processing, Universidad rey Juan Carlos (URJC), 28942 Madrid, SpainDepartment of Statistics, Universidad Carlos III de Madrid (UC3M), 28911 Madrid, SpainDepartment of Statistics, Universidad Carlos III de Madrid (UC3M), 28911 Madrid, SpainDepartment of Signal Processing, Universidad Carlos III de Madrid (UC3M), 28911 Madrid, SpainDepartment of Signal Processing, Universidad Carlos III de Madrid (UC3M), 28911 Madrid, SpainWe 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.https://www.mdpi.com/2227-7390/9/7/784Bayesian inferenceimportance samplingMCMCinversion problems |
| spellingShingle | Luca Martino Fernando Llorente Ernesto Curbelo Javier López-Santiago Joaquín Míguez Automatic Tempered Posterior Distributions for Bayesian Inversion Problems Mathematics Bayesian inference importance sampling MCMC inversion problems |
| title | Automatic Tempered Posterior Distributions for Bayesian Inversion Problems |
| title_full | Automatic Tempered Posterior Distributions for Bayesian Inversion Problems |
| title_fullStr | Automatic Tempered Posterior Distributions for Bayesian Inversion Problems |
| title_full_unstemmed | Automatic Tempered Posterior Distributions for Bayesian Inversion Problems |
| title_short | Automatic Tempered Posterior Distributions for Bayesian Inversion Problems |
| title_sort | automatic tempered posterior distributions for bayesian inversion problems |
| topic | Bayesian inference importance sampling MCMC inversion problems |
| url | https://www.mdpi.com/2227-7390/9/7/784 |
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