Phylogenetic inference using Hamiltonian Monte Carlo

Ph. D. Thesis.Phylogenetics is the study of evolutionary structure, aiming to reconstruct the branching structure of speciation from a common ancestor. There are many methods of infering the tree-like structure from the most basic, physical traits (morphology) to analysing the distances between genetic code based on a prede ned metric. For viruses such a method is the best way to access their hereditity. Bayesian inference enables us to learn a region of possible trees and alter the distribution of trees according to prior beliefs. The most common method of conducting Bayesian inference over evolutionary trees, called Tree space (Billera et al., 2001), is by Markov Chain Monte Carlo (MCMC). Tree space is big and exploration is slow; a modern technique for speeding up MCMC is Hamiltonian Monte Carlo (HMC), developed by Duane et al. (1987). We incorporate HMC into Tree space by creating our own algorithm: Cross-Orthant HMC (COrtHMC). Many methods of increasing HMC convergence speed have been developed, such as Riemannian Manifold HMC (RM-HMC) (Girolami et al., 2011). Where applicable, we adapted such methods to COrtHMC and then compared COrtHMC to pre-existing methods of phylogenetic inference and probabilistic path HMC (Dinh et al., 2017). We found that all forms of COrtHMC perform similarly, including ppHMC, but that the increased computational cost in using such HMC methods outweighs any bene t.EPSR