A Nonparametric Bayesian Approach to Inverse Problems
Robert L. Wolpert, K. Hansen · 2003
Abstract We propose a new method for making inference about an unknown measure Γ (d λ) upon observing some values of the Fredholm integral g(w) = f k(w, λ)T(d λ) of a known kernel k(w, A), using Levy random fields as Bayesian prior distributions for modelling uncertainty about T(d λ). Inference is based on simulation-based MCMC methods. The method is illustrated with a problem in polymer chemistry.