Random sampling from joint probability distributions defined in a bayesian framework

Overview & Synopsis

Random variables characterized by a joint probability distribution function (jpdf) defined in a Bayesian framework are generally sampled with Markov chain Monte Carlo (MCMC). The latter can be computationally demanding when the number of variables is high. As an alternative , the maximal conditional probability distribution (MCPD) sampler was recently introduced by some of the authors of the present article to readily and efficiently draw values randomly sampled from the desired jpdf. The MCPD approach provides the probability distribution of a given variable under the condition that the other variables maximized the conditional jpdf. However, contrarily to MCMC, MCPD does not provide enough draws to allow posterior uncertainty and sensitivity analyses of the computer model responses. In the present work, we show how to draw random samples from the MCPD draws under the requirement that the target jpdf possesses a particular dependence structure. Several numerical tests are carried out to prove the efficiency of the new sampling method. The new approach is used to perform the predictive uncertainty and sensitivity analyses of numerical models posterior to their statistical calibration from experimental data.