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testing if seqs. are in same phylo. tree?

Spencer Muse muse at kurtz.bio.psu.edu
Fri Nov 10 19:19:14 EST 1995


ednah at mws4.biol.berkeley.edu (Huelsenbeck) wrote:
>
> Because the null hypothesis is a subset of the alternative 
> hypothesis, this ratio should be asymptotically distributed as a Chi 
> square probability density distribution with (n ­ m) degrees of 
> freedom

 John,

 Perhaps I'm misunderstanding something. The topologies aren't really 
 proper parameters in the classical sense, so I don't see why you 
 would expect an asymptotic chi-square. If I have two genes for each
 of four taxa, it seems to me that I have 5p (5 branches times the
 number of parameters per branch) parameters for each gene tree. Under
 the full model I might have 10p parameters (5p for each gene). It
 also seems that this is the case under the null. We don't add 2 
 parameters for the two topologies under the full model, and one for
 the single topology under the null or something like that. This 
 problem seems analagous to that of testing two competing topologies.
 Please clear this part up for me.

 Having said that, it is, of course, of no concern since we must use
 a Monte Carlo approach to evaluate the p-values anyway. And as 
 another somewhat irrelevant aside, it seems that Goldman's claim
 about the unsuitability of the chi-squaare approximation was a bit
 too strong. A number of us have found this approximation to be quite 
 good when yop have fully-specified null and alternative models. I
 think that slight correction might have even popped up in a Goldman
 and Yang paper somewhere along the way.

 Spencer Muse



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