Bayesian inverse problems in measure spaces with application to Burgers and Hamilton–Jacobi equations with white noise forcing
Hoang, Viet Ha.
Date of Issue2012
School of Physical and Mathematical Sciences
This paper formulates Bayesian inverse problems for inference in a topological measure space given noisy observations. Conditions for the validity of the Bayes’ formula and the well posedness of the posterior measure are studied. The abstract theory is then applied to Burgers and Hamilton–Jacobi equations on a semi-infinite time interval with forcing functions which are white noise in time. Inference is made on the white noise forcing, assuming the Wiener measure as the prior.
© 2012 IOP Publishing Ltd. This paper was published in Inverse Problems and is made available as an electronic reprint (preprint) with permission of IOP Publishing Ltd. The paper can be found at the following official DOI: [http://dx.doi.org/10.1088/0266-5611/28/2/025009]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.