An Auto-Validating, Trans-Dimensional, Universal Rejection Sampler for Locally Lipschitz Arithmetical Expressions
Raazesh Sainudiin, A. York · 2013
The sample space of a trans-dimensional random vector is a union of spaces with different dimensions. We introduce a trans-dimensional extension of the rejection sampler of von Neumann. Our construction of the rejection sampler is based on interval analysis and provides a universal method that is capable of producing independent and identically distributed (IID) samples from a large class of trans-dimensional target densities with locally Lipschitz arithmetical expressions. We illustrate the efficiency of the sampler by theory and by examples in up to ten dimensions. Our sampler is immune to the ‘pathologies’ of some infamous densities that were previously considered unsamplable and can rigorously draw IID trans-dimensional posterior samples from small binomial partition models and phylogenetic tree spaces.