Hybrid Samplers for Ill-posed Inverse
Problems
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. In this talk we investigate the convergence
properties of the random-scan random walk Metropolis (RSM) algorithm 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 when estimating
the coefficients of a partial differential equation in a Bayesian framework.