Spectral likelihood expansions for Bayesian inference

Abstract : A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.
Document type :
Journal articles
Liste complète des métadonnées

Cited literature [114 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01432170
Contributor : Noura Fajraoui <>
Submitted on : Wednesday, January 11, 2017 - 3:46:12 PM
Last modification on : Tuesday, March 5, 2019 - 9:30:12 AM
Document(s) archivé(s) le : Friday, April 14, 2017 - 1:13:35 PM

File

RSUQ-2015-004.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Joseph B. Nagel, B Sudret. Spectral likelihood expansions for Bayesian inference. Journal of Computational Physics, Elsevier, 2016, 309, pp.267 - 294. 〈10.1016/j.jcp.2015.12.047〉. 〈hal-01432170〉

Share

Metrics

Record views

71

Files downloads

58