  A new algorithm is developed to tackle the issue of sampling non-Gaussian
model parameter posterior probability distributions that arise from solutions
to Bayesian inverse problems. The algorithm aims to mitigate some of the
hurdles faced by traditional Markov Chain Monte Carlo (MCMC) samplers, through
constructing proposal probability densities that are both, easy to sample and
that provide a better approximation to the target density than a simple
Gaussian proposal distribution would. To achieve that, a Gaussian proposal
distribution is augmented with a Gaussian Process (GP) surface that helps
capture non-linearities in the log-likelihood function. In order to train the
GP surface, an iterative approach is adopted for the optimal selection of
points in parameter space. Optimality is sought by maximizing the information
gain of the GP surface using a minimum number of forward model simulation runs.
The accuracy of the GP-augmented surface approximation is assessed in two ways.
The first consists of comparing predictions obtained from the approximate
surface with those obtained through running the actual simulation model at
hold-out points in parameter space. The second consists of a measure based on
the relative variance of sample weights obtained from sampling the approximate
posterior probability distribution of the model parameters. The efficacy of
this new algorithm is tested on inferring reaction rate parameters in a 3-node
and 6-node network toy problems, which imitate idealized reaction networks in
combustion applications.
