Published 09/07/2018
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Spectral likelihood expansions for bayesian inference

B.Sudret , J.B.

Keywords
Introduction
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A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probabilitydensity. The starting point is a series expansion of the likelihood function in terms of orthogonalpolynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculatedsemi-analytically. The posterior is formally represented as the product of a reference density and a linearcombination of polynomial basis functions. Both the model evidence and the posterior moments are relatedto the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows oneto make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussedand demonstrated on the basis of simple applications from classical statistics and inverse modeling.
Method
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