An Auto-validating Rejection Sampler for Differentiable Arithmetical Expressions: Posterior Sampling of Phylogenetic Quartets

  • Raazesh SainudiinEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 539)


We introduce an efficient extension of a recently introduced auto-validating rejection sampler that is capable of producing independent and identically distributed (IID) samples from a large class of target densities with locally Lipschitz arithmetical expressions. Our extension is restricted to target densities that are differentiable. We use the centered form, as opposed to the natural interval extension, to get tighter range enclosures of the differentiable multivariate target density using interval extended gradient differentiation arithmetic. By using the centered form we are able to sample one hundred times faster from the posterior density over the space of phylogenetic trees with four leaves (quartets).


interval analysis centered form phylogentic inference 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Laboratory for Mathematical Statistical Experiments and, Department of Mathematics and StatisticsUniversity of CanterburyChristchurchNew Zealand

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