Drummond, AFewster, RSuchard, MWu, Chieh-Hsi2014-11-2320142014http://hdl.handle.net/2292/23560When inferring a phylogeny in a probabilistic framework, one is faced with many choices of how to model the underlying processes that give rise to the observed data. This includes how to accommodate the across-site variation in the properties of the nucleotide substitution process and how to incorporate the across-time variation in the parameters of the tree-generating process. To model across-site heterogeneity in the properties of the nucleotide substitution process, one commonly pre-de nes the partition scheme of the alignment thereby grouping sites into a number of categories and then independently estimates the substitution model of each category. This practice ignores the uncertainty associated with the partition scheme, and the pre-de ned partition scheme may not agree with the data. This thesis rst presents three new methods that accommodate the uncertainty associated with the partition scheme. They estimate the number of categories, the assignments of sites to the categories, the nucleotide substitution model and the site rate model for each category, and the uncertainty in these selections. These methods employ approaches of Bayesian model selection and/or Bayesian nonparametrics. They di er in the a priori assumptions on the assignments of sites to categories, and therefore provide di erent views on the across-site heterogeneity in the properties of the nucleotide substitution process. Analyses with all three methods have found statistical evidence for across-site heterogeneity in the nucleotide substitution process both within a single gene and among genes in various sets of empirical data. Recently proposed models based on the birth-death-sampling process allow the rate parameters of birth, death and sampling events to vary through time as piecewise constant functions, but require the number of rate shifts to be xed a priori. This thesis presents a new method that employs a transdimensional sampling algorithm for Bayesian model selection to directly estimate the number of shifts in the parameters of the birth-death-sampling process (or epidemiological parameters in the case of a phylogeny of a rapidly evolving infectious disease). In summary, I have developed a series of new phylogenetic methods based on Bayesian model selection and Bayesian nonparametrics to permit the direct inference of the across-site variation of the nucleotide substitution process and the acrosstime variation in the birth-death-sampling process. These new methods take into account the uncertainty associated with the alignment partition scheme and the tree generating process, avoiding potential model misspeci cation.Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher.https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htmhttp://creativecommons.org/licenses/by-nc-sa/3.0/nz/ThesisCopyright: The Authorhttp://purl.org/eprint/accessRights/OpenAccessQ112907732