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We consider probabilistic programming for birth-death models of evolution andintroduce a new widely-applicable inference method that combines an extensionof the alive particle filter (APF) with automatic Rao-Blackwellization viadelayed sampling. Birth-death models of evolution are an important family ofphylogenetic models of the diversification processes that lead to evolutionarytrees. Probabilistic programming languages (PPLs) give phylogeneticists a newand exciting tool: their models can be implemented as probabilistic programswith just a basic knowledge of programming. The general inference methods inPPLs reduce the need for external experts, allow quick prototyping and testing,and accelerate the development and deployment of new models. We show how thesebirth-death models can be implemented as simple programs in existing PPLs, anddemonstrate the usefulness of the proposed inference method for such models.For the popular BiSSE model the method yields an increase of the effectivesample size and the conditional acceptance rate by a factor of 30 in comparisonwith a standard bootstrap particle filter. Although concentrating onphylogenetics, the extended APF is a general inference method that shows itsstrength in situations where particles are often assigned zero weight. In thecase when the weights are always positive, the extra cost of using the APFrather than the bootstrap particle filter is negligible, making our method asuitable drop-in replacement for the bootstrap particle filter in probabilisticprogramming inference.

Probabilistic programming for birth-death models of evolution using an alive particle filter with delayed sampling