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Investigating Convergence of Markov Chain Monte Carlo Methods for Bayesian Phylogenetic Inference

Spade, David Allen
http://rave.ohiolink.edu/etdc/view?acc_num=osu1372173121

Abstract Details

2013, Doctor of Philosophy, Ohio State University, Statistics.
In biology, it is commonly of interest to investigate the evolutionary pattern that gave rise to an existing group of individuals, such as species or genes. This pattern is most often represented pictorially by a phylogenetic tree. Many methods of inferring evolutionary patterns have been proposed, but as advances in computational capabilities have made Bayesian inference more approachable, it has become an increasingly popular technique for phylogenetic inference. In Bayesian inference, it is often the case that the posterior density cannot be written out in its entirety due to the intractability of the normalizing constant. One way of working around this is to use a Markov chain Monte Carlo (MCMC) method. The idea is that after several (possibly many) iterations, the chain has approximately converged to its stationary distribution, namely, the posterior distribution. After these initial iterations, subsequent steps of the chain represent an approximate sample from the posterior distribution, thus enabling Bayesian inference. The biggest question one faces when using MCMC methods is the question of how long the chain should be run before sampling can begin, i.e., the mixing time of the chain. Many methods exist that aim to answer this question by using the output of the chain, but these methods can only give indications that the chain has not converged. They cannot be used to conclude that a Markov chain has converged. In this dissertation, we first provide upper bounds on the mixing times of two distinct Markov chains. Both chains move about the space of rooted phylogenetic tree topologies. We also explore methods of bounding the mixing time for a special case of the Metropolis-Hastings algorithm for inference of the branch lengths of a phylogenetic tree given the tree topology. We first provide an upper bound on the mixing time through analytical methods. When this provides results that do not give a helpful upper bound on the mixing time, we present a Monte Carlo method. The Monte Carlo method of bounding the mixing time also gives results that do not lead to a helpful upper bound, but it does provide a substantial improvement over the analytical methods. This represents a step forward in the pursuit of an upper bound on the mixing time of a specific MCMC algorithm for Bayesian inference of the branch lengths of a phylogenetic tree.
Radu Herbei, Ph.D. (Advisor)
Laura S. Kubatko, Ph.D. (Advisor)
Steven N. MacEachern, Ph.D. (Committee Member)
Dennis K. Pearl, Ph.D. (Committee Member)
200 p.
Evolution and Development; Statistics
Markov Chain Monte Carlo; Phylogenetics; Bayesian Inference; Convergence; Mixing Time

Recommended Citations

Citations

  • Spade, D. A. (2013). Investigating Convergence of Markov Chain Monte Carlo Methods for Bayesian Phylogenetic Inference [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1372173121

    APA Style (7th edition)

  • Spade, David. Investigating Convergence of Markov Chain Monte Carlo Methods for Bayesian Phylogenetic Inference. 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1372173121.

    MLA Style (8th edition)

  • Spade, David. "Investigating Convergence of Markov Chain Monte Carlo Methods for Bayesian Phylogenetic Inference." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1372173121

    Chicago Manual of Style (17th edition)

osu1372173121
815
© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.