Spectral likelihood expansions for Bayesian inference

Authors

Nagel, J. B. and Sudret, B.

Abstract

A spectral approach to Bayesian inference is presented. It is based on the idea of computing a series expansion of the likelihood function in terms of polynomials that are orthogonal with respect to the prior. Based on this spectral likelihood expansion, the posterior density and all statistical quantities of interest can be calculated semi-analytically. 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.