Randomized maximum likelihood based posterior sampling

Minimization of a stochastic cost function is commonly used for approximate sampling in high-dimensional Bayesian inverse problems with Gaussian prior distributions and multimodal posterior distributions. The density the samples generated by minimization not desired target density, unless observation operator linear, but distribution useful as proposal importance or Markov chain Monte Carlo methods. In this paper, we focus on applications to from high dimensions. We first show that improved computing all critical points instead only minimizers objective function. For geoscience problems, demonstrate an efficient weighting uses low-rank Gauss-Newton approximation determinant Jacobian. method applied two toy known Darcy flow problem multiple modes posterior.