Norges Teknisk-naturvitenskapelige Universitet Directional Metropolis–hastings Updates for Posteriors with Nonlinear Likelihoods Directional Metropolis–hastings Updates for Posteriors with Nonlinear Likelihoods

In this paper we consider spatial problems modeled by a Gaussian random field prior density and a nonlinear likelihood function linking the hidden variables to the observed data. We define a directional block Metropolis–Hastings algorithm to explore the posterior density. The method is applied to seismic data from the North Sea. Based on our results we believe it is important to assess the actual posterior in order to understand possible shortcomings of linear approximations.