Simulating a Random Vector Conditionally to a Subvariety: A Generic Dichotomous Approach

Abstract

The problem of sampling a random vector conditionnaly to a subvariety within a box (actually, a small volume around the subvariety) is addressed. The approach is generic, in the sense that the subvariety may be defined by an isosurface related to any (computable) continuous function. Our approach is based on a dichotomous method. As a result, the sampling process is straightforward, accurate and avoids the use of MCMC methods. Our implementation relies on the evaluation of the matching with the subvariety at each dichotomy step. By using interval analysis techniques for evaluating the matching, our method has been applied up to the dimension 11. Perspectives are evoked for improving the sampling efficiency on higher dimensions. A concept and an example of application of this simulation technique to black-box function optimization are detailed.