Inverse Problems and a Lévy Process Solution
Martin B. Hansen, Katja Ickstadt and Robert L. Wolpert
Aalborg Universitet, Duke University and Technische
Universität Darmstadt
August 2000
We propose a new method of making inference about an unknown measure
F(ds) upon observing some values of the integral g(x)=\int k(x,s)
F(ds) of a known kernal k(x,s), using Lévy processes as
Bayesian prior distributions for modeling uncertainty about
F(ds), using simulation-based MCMC methods. The methods are
illustrated with two problems in polymer chemistry.
Keywords: Lévy process, inference, inverse problem,
polymer.
A preliminary version of the manuscript is available
in postscript and
pdf formats.