  We develop a Bayesian inference method that allows the efficient
determination of several interesting parameters from complicated
high-energy-density experiments performed on the National Ignition Facility
(NIF). The model is based on an exploration of phase space using the
hydrodynamic code HYDRA. A linear model is used to describe the effect of
nuisance parameters on the analysis, allowing an analytic likelihood to be
derived that can be determined from a small number of HYDRA runs and then used
in existing advanced statistical analysis methods. This approach is applied to
a recent experiment in order to determine the carbon opacity and X-ray drive;
it is found that the inclusion of prior expert knowledge and fluctuations in
capsule dimensions and chemical composition significantly improve the agreement
between experiment and theoretical opacity calculations. A parameterisation of
HYDRA results is used to test the application of both Markov chain Monte Carlo
(MCMC) and genetic algorithm (GA) techniques to explore the posterior. These
approaches have distinct advantages and we show that both can allow the
efficient analysis of high energy density experiments.
