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Re: Dakotadon (non-hadrosauriform) revised



> 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