  We consider probabilistic programming for birth-death models of evolution and
introduce a new widely-applicable inference method that combines an extension
of the alive particle filter (APF) with automatic Rao-Blackwellization via
delayed sampling. Birth-death models of evolution are an important family of
phylogenetic models of the diversification processes that lead to evolutionary
trees. Probabilistic programming languages (PPLs) give phylogeneticists a new
and exciting tool: their models can be implemented as probabilistic programs
with just a basic knowledge of programming. The general inference methods in
PPLs reduce the need for external experts, allow quick prototyping and testing,
and accelerate the development and deployment of new models. We show how these
birth-death models can be implemented as simple programs in existing PPLs, and
demonstrate the usefulness of the proposed inference method for such models.
For the popular BiSSE model the method yields an increase of the effective
sample size and the conditional acceptance rate by a factor of 30 in comparison
with a standard bootstrap particle filter. Although concentrating on
phylogenetics, the extended APF is a general inference method that shows its
strength in situations where particles are often assigned zero weight. In the
case when the weights are always positive, the extra cost of using the APF
rather than the bootstrap particle filter is negligible, making our method a
suitable drop-in replacement for the bootstrap particle filter in probabilistic
programming inference.
