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*To*: dinosaur@usc.edu*Subject*: Re: Dakotadon (non-hadrosauriform) revised*From*: David Černý <david.cerny1@gmail.com>*Date*: Fri, 29 May 2015 21:45:09 -0700*In-reply-to*: <CAMR9O1J8mua76pN51ddHb7_P_aFuZyGTGpPXJOKkyP--aX94tA@mail.gmail.com>*References*: <CAMR9O1J8mua76pN51ddHb7_P_aFuZyGTGpPXJOKkyP--aX94tA@mail.gmail.com>*Reply-to*: david.cerny1@gmail.com*Sender*: owner-DINOSAUR@usc.edu

> The systematic relationships of Dakotadon lakotaensis are evaluated > using both the parsimony and posterior probability optimality criteria One minor quibble: it's incorrect to imply that Bayesian inference employs posterior probability as an optimality criterion. Unlike parsimony and maximum likelihood, which search the tree space for the best estimate (with no guarantee that they will be able to find it), the Metropolis-Hastings algorithm draws samples from the joint parameter distribution in proportion to their posterior probability. If the chain converges to the target distribution, the frequency of a particular parameter value (e.g., tree topology) within the collected sample will correspond to its posterior probability, integrated over all the possible values of every other parameter. Importantly, the sample doesn't have to contain the best estimate (i.e., the global maximum of the posterior probability density function) in order for this property to hold. There's in fact no reason at all to expect that the chain will sample the highest probability tree -- that's not what it's meant to do. Bayesian analysis yields a lot of good trees, but not (necessarily) the "best" one(s). Using the phrase "posterior probability optimality criterion" to describe a MrBayes analysis can even be outright misleading (in addition to being inaccurate), because there is a recently developed method which actually fits that description, unlike the MCMC samplers implemented in MrBayes or BEAST: Wheeler's (2013) MAP-A. There was also some debate about how to properly summarize the posterior sample of topologies from an MCMC run, with Wheeler & Pickett (2008) criticizing the widespread practice of using the majority-rule consensus. They wrote that "[a]s an optimality criterion to choose among candidate topologies, posterior probability is a fine option, but current use [i.e., using consensus trees] does not follow this path". Instead, they advocated picking the topology with the highest marginal posterior probability as a summary. The term "posterior probability optimality criterion" suggests that Boyd and Pagnac followed Wheeler and Pickett's proposal, but the text of their paper makes it clear that they used the standard consensus approach (which is great -- Wheeler and Pickett's arguments were highly flawed, as shown by Sukumaran & Linkem (2008)). Anyway, it's great that Bayesian analyses of Mesozoic dinosaurs are becoming more and more common; the method definitely has a lot of potential. *Refs:* Sukumaran J, Linkem CW 2008 Choice of topology estimators in Bayesian phylogenetic analysis. Mol Biol Evol 26(1): 1-3 Wheeler WC 2013 Maximum a posteriori probability assignment (MAP-A): an optimality criterion for phylogenetic trees via weighting and dynamic programming. Cladistics 30(3): 282-90 Wheeler WC, Pickett KM 2008 Topology-Bayes versus clade-Bayes in phylogenetic analysis. Mol Biol Evol 25(2): 447-53 -- David Černý

**References**:**Dakotadon (non-hadrosauriform) revised***From:*Ben Creisler <bcreisler@gmail.com>

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