  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.
