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Mathematical Medicine and Biology Advance Access originally published online on October 31, 2007
Mathematical Medicine and Biology 2007 24(4):401-411; doi:10.1093/imammb/dqm008
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Bayesian support is larger than bootstrap support in phylogenetic inference: a mathematical argument

Tom Britton{dagger}

Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden

Bodil Svennblad

Department of Mathematics, Uppsala University, Uppsala, Sweden

Per Erixon and Bengt Oxelman

Department of Systematic Botany, Uppsala University, Uppsala, Sweden

{dagger} E-mail: tomb{at}math.su.se

Received on May 2, 2006. Revised on June 25, 2007. Accepted on September 17, 2007.

In phylogenetic inference, the support of an estimated phylogenetic tree topology and its interior branches is usually measured either with non-parametric bootstrap support (BS) values or with Bayesian posterior probabilities (BPPs). Extensive empirical evidence indicates that BPP values are systematically larger than BS when measured on the same data set, but there are no theoretical results supporting such a systematic difference. In the present note, we give a heuristic mathematical argument supporting the empirically observed phenomenon. The argument uses properties of the marginal and profile likelihoods of the normal distribution. The heuristic arguments are supported in a simulation study evaluating different steps in the argument.

Keywords: Bayesian posterior probability; bootstrap support; marginal likelihood; phylogenetic inference; profile likelihood


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