We propose a new method for making inference about an unknown measure Γ(dλ) upon observing some values of the Fredholm integral g(ω)=∫ k(ω,λ) Γ(dλ) of a known kernel k(ω,λ), using Lévy random fields as Bayesian prior distributions for modeling uncertainty about Γ(dλ). Inference is based on simulation-based MCMC methods. The method is illustrated with a problem in polymer chemistry.

Keywords: Gamma process; Lévy process; polymer; random field; reversible jump MCMC; rheology

The manuscript is available in pdf (213 kb) format. Cite as:

@InCollection{Wolp:Icks:Hans:2003,
      Author = "Robert L. Wolpert and Katja Ickstadt and Martin
                B{\o}gsted Hansen",
       Title = "A Nonparametric {B}ayesian Approach to Inverse Problems
                (with discussion)",
   BookTitle = "Bayesian Statistics 7",
      Editor = "Jos{\'e} Miguel Bernardo and Maria Jesus Bayarri and
                James O. Berger and A. Phillip Dawid and David
                Heckerman and Adrian F. M. Smith and Mike West",
   Publisher = "Oxford University Press",
     Address = "Oxford, UK",
        ISBN = "0-19-852615-6",
       Pages = "403--418",
        Year = 2003,
}