Iterative Importance Sampling Algorithms for Parameter Estimation

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov chain Monte Carlo (MCMC) is often used for the numerical solution of such problems. An alternative to MCMC is importance sampling, which can exhibit near perfect scaling with the number of cores on high performance computing systems because samples are drawn independently. However, finding a suitable proposal distribution is a challenging task. Several sampling algorithms have been proposed over the past years that take an iterative approach to constructing a proposal distribution. We investigate the applicability of such algorithms by applying them to two realistic and challenging test problems, one in subsurface flow, and one in combustion modeling. More specifically, we implement importance sampling algorithms that iterate over the mean and covariance matrix of Gaussian or multivariate t-proposal distributions. Our implementation leverages massively parallel computers, and we present strategies to initialize the iterations using “coarse” MCMC runs or Gaussian mixture models.