Importance sampling for Bayesian sensitivity analysis

We examine the use of sensitivity analysis with a particular focus on calculating the bounds of imprecise previsions in Bayesian statistics. We explain the use of importance sampling in approximating the range of these imprecise previsions and we develop an approximation function for the imprecise posterior prevision based on generating a finite number of random variables. We develop a convergence theorem that shows that this approximation converges almost surely to the posterior prevision as we generate more and more random variables. We also develop a useful accuracy bound for the approximation for a large finite number of generated random variables. We test the efficiency of this approximation using a simple example involving the imprecise Dirichlet model.