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An Efficient Independence Sampler for Updating Branches in Bayesian Markov chain Monte Carlo Sampling of Phylogenetic Trees

Sampling tree space is the most challenging aspect of Bayesian phylogenetic inference. The sheer number of alternative topologies is problematic by itself. In addition, the complex dependency between branch lengths and topology increases the difficulty of moving efficiently among topologies. Current... Full description

Journal Title: Systematic Biology 2016-01-01, Vol.65 (1), p.161-176
Main Author: Aberer, Andre J
Other Authors: Stamatakis, Alexandros , Ronquist, Fredrik
Format: Electronic Article Electronic Article
Language: English
Subjects:
DNA
Quelle: Alma/SFX Local Collection
Publisher: England: Oxford University Press
ID: ISSN: 1063-5157
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title: An Efficient Independence Sampler for Updating Branches in Bayesian Markov chain Monte Carlo Sampling of Phylogenetic Trees
format: Article
creator:
  • Aberer, Andre J
  • Stamatakis, Alexandros
  • Ronquist, Fredrik
subjects:
  • Algorithms
  • Bayes Theorem
  • Bayesian analysis
  • Bayesian inference
  • Bioinformatics (Computational Biology)
  • Bioinformatik (beräkningsbiologi)
  • Branches
  • Classification - methods
  • Computer and Information Sciences
  • Computer Simulation
  • Data- och informationsvetenskap
  • Datasets
  • Diversity of life
  • DNA
  • independence sampling
  • Livets mångfald
  • Markov analysis
  • Markov chain Monte Carlo
  • Markov Chains
  • Models, Theoretical
  • Monte Carlo Method
  • Monte Carlo simulation
  • Natural Sciences
  • Naturvetenskap
  • Newton
  • Newton-Raphson optimization
  • Phylogenetics
  • Phylogeny
  • proposal efficiency
  • Raphson optimization
  • Regular
  • Regular Articles
  • Sampling
  • Skewed distribution
  • Standard deviation
  • T distribution
  • Taxa
  • Topology
  • tree topology proposals
ispartof: Systematic Biology, 2016-01-01, Vol.65 (1), p.161-176
description: Sampling tree space is the most challenging aspect of Bayesian phylogenetic inference. The sheer number of alternative topologies is problematic by itself. In addition, the complex dependency between branch lengths and topology increases the difficulty of moving efficiently among topologies. Current tree proposals are fast but sample new trees using primitive transformations or re-mappings of old branch lengths. This reduces acceptance rates and presumably slows down convergence and mixing. Here, we explore branch proposals that do not rely on old branch lengths but instead are based on approximations of the conditional posterior. Using a diverse set of empirical data sets, we show that most conditional branch posteriors can be accurately approximated via a Γ distribution. We empirically determine the relationship between the logarithmic conditional posterior density, its derivatives, and the characteristics of the branch posterior. We use these relationships to derive an independence sampler for proposing branches with an acceptance ratio of ~90% on most data sets. This proposal samples branches between 2× and 3× more efficiently than traditional proposals with respect to the effective sample size per unit of runtime. We also compare the performance of standard topology proposals with hybrid proposals that use the new independence sampler to update those branches that are most affected by the topological change. Our results show that hybrid proposals can sometimes noticeably decrease the number of generations necessary for topological convergence. Inconsistent performance gains indicate that branch updates are not the limiting factor in improving topological convergence for the currently employed set of proposals. However, our independence sampler might be essential for the construction of novel tree proposals that apply more radical topology changes.
language: eng
source: Alma/SFX Local Collection
identifier: ISSN: 1063-5157
fulltext: fulltext
issn:
  • 1063-5157
  • 1076-836X
  • 1076-836X
url: Link


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titleAn Efficient Independence Sampler for Updating Branches in Bayesian Markov chain Monte Carlo Sampling of Phylogenetic Trees
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creatorcontribAberer, Andre J ; Stamatakis, Alexandros ; Ronquist, Fredrik
descriptionSampling tree space is the most challenging aspect of Bayesian phylogenetic inference. The sheer number of alternative topologies is problematic by itself. In addition, the complex dependency between branch lengths and topology increases the difficulty of moving efficiently among topologies. Current tree proposals are fast but sample new trees using primitive transformations or re-mappings of old branch lengths. This reduces acceptance rates and presumably slows down convergence and mixing. Here, we explore branch proposals that do not rely on old branch lengths but instead are based on approximations of the conditional posterior. Using a diverse set of empirical data sets, we show that most conditional branch posteriors can be accurately approximated via a Γ distribution. We empirically determine the relationship between the logarithmic conditional posterior density, its derivatives, and the characteristics of the branch posterior. We use these relationships to derive an independence sampler for proposing branches with an acceptance ratio of ~90% on most data sets. This proposal samples branches between 2× and 3× more efficiently than traditional proposals with respect to the effective sample size per unit of runtime. We also compare the performance of standard topology proposals with hybrid proposals that use the new independence sampler to update those branches that are most affected by the topological change. Our results show that hybrid proposals can sometimes noticeably decrease the number of generations necessary for topological convergence. Inconsistent performance gains indicate that branch updates are not the limiting factor in improving topological convergence for the currently employed set of proposals. However, our independence sampler might be essential for the construction of novel tree proposals that apply more radical topology changes.
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subjectAlgorithms ; Bayes Theorem ; Bayesian analysis ; Bayesian inference ; Bioinformatics (Computational Biology) ; Bioinformatik (beräkningsbiologi) ; Branches ; Classification - methods ; Computer and Information Sciences ; Computer Simulation ; Data- och informationsvetenskap ; Datasets ; Diversity of life ; DNA ; independence sampling ; Livets mångfald ; Markov analysis ; Markov chain Monte Carlo ; Markov Chains ; Models, Theoretical ; Monte Carlo Method ; Monte Carlo simulation ; Natural Sciences ; Naturvetenskap ; Newton ; Newton-Raphson optimization ; Phylogenetics ; Phylogeny ; proposal efficiency ; Raphson optimization ; Regular ; Regular Articles ; Sampling ; Skewed distribution ; Standard deviation ; T distribution ; Taxa ; Topology ; tree topology proposals
ispartofSystematic Biology, 2016-01-01, Vol.65 (1), p.161-176
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descriptionSampling tree space is the most challenging aspect of Bayesian phylogenetic inference. The sheer number of alternative topologies is problematic by itself. In addition, the complex dependency between branch lengths and topology increases the difficulty of moving efficiently among topologies. Current tree proposals are fast but sample new trees using primitive transformations or re-mappings of old branch lengths. This reduces acceptance rates and presumably slows down convergence and mixing. Here, we explore branch proposals that do not rely on old branch lengths but instead are based on approximations of the conditional posterior. Using a diverse set of empirical data sets, we show that most conditional branch posteriors can be accurately approximated via a Γ distribution. We empirically determine the relationship between the logarithmic conditional posterior density, its derivatives, and the characteristics of the branch posterior. We use these relationships to derive an independence sampler for proposing branches with an acceptance ratio of ~90% on most data sets. This proposal samples branches between 2× and 3× more efficiently than traditional proposals with respect to the effective sample size per unit of runtime. We also compare the performance of standard topology proposals with hybrid proposals that use the new independence sampler to update those branches that are most affected by the topological change. Our results show that hybrid proposals can sometimes noticeably decrease the number of generations necessary for topological convergence. Inconsistent performance gains indicate that branch updates are not the limiting factor in improving topological convergence for the currently employed set of proposals. However, our independence sampler might be essential for the construction of novel tree proposals that apply more radical topology changes.
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36Taxa
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abstractSampling tree space is the most challenging aspect of Bayesian phylogenetic inference. The sheer number of alternative topologies is problematic by itself. In addition, the complex dependency between branch lengths and topology increases the difficulty of moving efficiently among topologies. Current tree proposals are fast but sample new trees using primitive transformations or re-mappings of old branch lengths. This reduces acceptance rates and presumably slows down convergence and mixing. Here, we explore branch proposals that do not rely on old branch lengths but instead are based on approximations of the conditional posterior. Using a diverse set of empirical data sets, we show that most conditional branch posteriors can be accurately approximated via a Γ distribution. We empirically determine the relationship between the logarithmic conditional posterior density, its derivatives, and the characteristics of the branch posterior. We use these relationships to derive an independence sampler for proposing branches with an acceptance ratio of ~90% on most data sets. This proposal samples branches between 2× and 3× more efficiently than traditional proposals with respect to the effective sample size per unit of runtime. We also compare the performance of standard topology proposals with hybrid proposals that use the new independence sampler to update those branches that are most affected by the topological change. Our results show that hybrid proposals can sometimes noticeably decrease the number of generations necessary for topological convergence. Inconsistent performance gains indicate that branch updates are not the limiting factor in improving topological convergence for the currently employed set of proposals. However, our independence sampler might be essential for the construction of novel tree proposals that apply more radical topology changes.
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