ML scores

Kent Holsinger kent at darwin.eeb.uconn.edu
Thu Aug 31 07:20:20 EST 2000

>>>>> "Mary" == Mary K Kuhner <mkkuhner at kingman.genetics.washington.edu> writes:

    Mary> "The probability of the tree given the data" would be "how
    Mary> frequently would I find this tree if I examined all
    Mary> evolutionary scenarios leading to this data?"  and can only
    Mary> be calculated if you are willing to assume something about
    Mary> the prior distribution of trees and use a Bayesian approach.
    Mary> Likelihood fans tend to reject the idea that we can know
    Mary> what the prior on trees is.

I don't see the pure likelihood and Bayesian approaches as being all
that different, since we can often make reasonable Bayesian inferences
based on vague prior information.

    P(tree|data) <is proportional to> P(data|tree) P(tree) , 

where P(data|tree) is, of course, the standard likelihood. In other
contexts, the likelihood "dominates" the posterior, P(tree|data), when
you've collected a reasonable amount of data. By dominates I mean that
the shape of the posterior distribution, P(tree|data), is insensitive
to the choice of priors. I expect the same to be true for phylogenetic
analyses, though I'm cautious enough to admit that the vastness of
tree space could lead to problems different from those encountered in
the typical point and interval estimation problems statisticians have
studied. In particular, I have no idea how much data an investigator
would have to collect for the likelihood to dominate the posterior. I
suspect we'll know in a few years, but we don't know right now.


Kent E. Holsinger                kent at darwin.eeb.uconn.edu
-- Department of Ecology & Evolutionary Biology          
-- University of Connecticut, U-3043                                       
-- Storrs, CT   06269-3043                                               

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