Bayesian Inverse Problems in PDEs
Andrew Stuart, Warwick

In this talk I willframe a range of inverse problems, all arising from the conjunction of differential equations and data, using a Bayesian approach  on function space.  I will prove a  well-posedness result for the inverse problem,  and use this well-posedness to prove a result relating approximation in the forward operator to approximation of the posterior measure for the inverse problem. I will also show that the Bayesian framework leads directly to an existence result for the related variational (optimal control) problem of maximizing the posterior probability. Applications in fluid mechanics and subsurface geophysics will be given.

An overview of the work may be found at: http://www.warwick.ac.uk/~masdr/acta2010.pdf