Title: DrSMC: A Sequential Monte Carlo Sampler for Deterministically Related Variables; Phylogenetic Inference with Divide and Conquer Sequential Monte Carlo (D&C SMC)

Talk by Neil Spencer (11am - 11:30am)

Title:  DrSMC: A Sequential Monte Carlo Sampler for Deterministically Related Variables

Abstract:  Computing posterior distributions over variables linked by deterministic constraints is a recurrent problem in Bayesian analysis. Such problems can arise due to censoring, identifiability issues, or other considerations. It is well-known that standard implementations of Monte Carlo methods break down in the presence of these deterministic relationships. Although several alternative Monte Carlo methods have been recently developed, few are applicable to deterministic relationships on continuous random variables. My Masters thesis work involved the development of a new Sequential Monte Carlo Sampler, called DrSMC, for such problems. In this talk, I discuss applying DrSMC to compute the posterior distribution of a continuous random vector given its sum.

Talk by Sean Jewell (11:30am - 12pm)

Title:  Phylogenetic Inference with Divide and Conquer Sequential Monte Carlo (D&C SMC)

Abstract:  Recently reconstructing evolutionary histories has become a computational issue due to the increased availability of genetic sequencing data and relaxations of classical modelling assumptions. My master's thesis focused on specializing a D&C SMC inference algorithm to phylogenetics to address these challenges. In phylogenetics, the tree structure used to represent evolutionary histories provides the model decomposition for D&C SMC. In particular, speciation events are used to recursively decompose the model into subproblems. Each subproblem is approximated by an independent population of weighted particles, which are merged and propagated to create an ancestral population. This approach provides the flexibility to relax classical assumptions on large trees by parallelizing these recursions.