Computing minimal-volume credible sets using interval analysis; application to bayesian estimation

Given a random vector p with a probability density function (pdf) pi(p), a credible set pi(p) with level alpha is a set that contains p with a probability alpha. The problem of characterizing minimal-volume credible sets (which correspond to level sets for pi) is considered. It is only assumed that the expression of pi(p) results from a combination of elementary operators (+,-,*,/) and elementary functions (sin, cos, abs, etc.). This paper provides an algorithm able to compute accurate inner and outer approximations of minimal-volume credible sets, in a guaranteed way. The approach is based on interval analysis and an application to nonlinear parameter estimation, in a Bayesian context, is treated. A windows solver associated with the presented algorithm is made available at http://www.ensieta.fr/e3i2/Jaulin/bayes.zip