Bayesian Phylogenetic Inference

Abstract: In this thesis we consider two very different topics in Bayesian phylogenetic inference. The first paper, "Inferring speciation and extinction rates under different sampling schemes" by Sebastian Höhna, Tanja Stadler, Fredrik Ronquist and Tom Britton, focuses on estimating the rates of speciation and extinction of species when only a subsample of the present day species is available. The second paper "Burnin Estimation and Convergence Assessment" by Sebastian Höhna and Kristoffer Sahlin focuses on how to analyze the output of Markov chain Monte Carlo (MCMC) runs with respect to convergence to the stationary distribution and approximation of the posterior probability distribution.The birth-death process is used to describe the evolution of species diversity. Previous work enabled the estimation of speciation and extinction rates under the assumption of a constant rate birth-death process and complete sampling of all extant species. We extend the complete sampled birth-death process to incomplete sampling with three different types of sampling schemes: random sampling, diversified sampling and clustered sampling. On a set of empirical phylogenies with known sampling fraction we observe that taking the sampling fraction into account gives better fitting models, either by random sampling or diversified sampling.The current trend in Bayesian phylogenetic inference is to extend the available models by using more complex models and/or hierarchical models. This renders Bayesian inference by means of the MCMC algorithm very intricate. Performance of single or multiple MCMC runs need to be assessed. We investigate which methods are used in Bayesian phylogenetics to assess the performance of MCMC runs, which methods are available from other research areas and compile a strategy on how to assess convergence and how to estimate the burnin automatically in a statistically sound framework.