  This article describes a method for using optimization to derive efficient
independent transition functions for Markov chain Monte Carlo simulations. Our
interest is in sampling from a posterior density $\pi(x)$ for problems in which
the dimension of the model space is large, $\pi(x)$ is multimodal with regions
of low probability separating the modes, and evaluation of the likelihood is
expensive. We restrict our attention to the special case for which the target
density is the product of a multivariate Gaussian prior and a likelihood
function for which the errors in observations are additive and Gaussian.
