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justification for "maximum maximum likelihood"

Joe Felsenstein joe at evolution.genetics.washington.edu
Sat Jul 19 01:05:05 EST 1997

In article <33CF66D6.7BC1 at evol5.mbl.edu>,
Andrew J. Roger <roger at evol5.mbl.edu> wrote:
>I was wondering if anyone has an up to date take on the debate between
>Felsenstein and Sober regarding how one comes up with nuisance
>parameters (such as branch lengths or any parameter in
>the model) during maximum likelihood analysis.
>... What if for most of the possible values for parameter
>P, Pr(Data| tree A, model, P) < Pr(Data| tree B, model, p),
>but only at the maxima of the two likelihood curves does tree A 
>confer a higher probability on the data.  Wouldn't one want to say
>that overall tree B is a better choice that tree A?

I can tell you that I haven't changed my position.  If at the
maximum A has the higher likelihood then you should prefer it.  I suppose
a Bayesian would feel differently.  Dunno what Elliott thinks about it
these days -- he has been working on other issues such as levels of
selection.  I had lunch with him two months ago but this didn't come up.

By the way, whether one regards branch lengths as nuisance parameters
depends on what you are trying to estimate -- the topology only, or
the topology plus branch lengths.

PS There has been a sudden reduction of Spam in the BIOSCI groups --
my congratulations to the BIOSCI management for putting some Spam-
blocking systems in place (I think).

Joe Felsenstein         joe at genetics.washington.edu     (IP No.
 Dept. of Genetics, Univ. of Washington, Box 357360, Seattle, WA 98195-7360 USA

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