In the Bayesian approach to ill-posed inverse problems, regularization
is imposed by specifying a prior distribution on the parameters of
interest and MCMC samplers are used to extract information about its
posterior distribution. The aim of this paper is to investigate the
convergence properties of the random-scan random walk Metropolis (RSM)
for posterior distributions in ill-posed inverse problems. We provide
an accessible set of sufficient conditions, in terms of the
observational model and the prior, to ensure geometric ergodicity of
RSM samplers of the posterior distribution. We illustrate how these
conditions can be checked in an application to the inversion of
oceanographic tracer data.
Meet the speaker in Room 212 Cockins Hall after the talk. Refreshments will be served.