[Fwd: Re: Probabilities on Phylogenetic Trees]

Richard Zander bryo at COMMTECH.NET
Tue Sep 16 14:38:51 CDT 1997


Tom DiBenedetto wrote:
>
>  Richard Zander wrote:
(Snip
> But
> given that there are 6 billion potential murderers in this world, at
> some scale you could consider that to be a low-probability result.
> But of course, you go out to collect evidence precisely for the
> purpose of narrowing the scale of your possibilities. Instead of 6
> billion, you narrow the scope down to those who had no alibi, those
> who were being blackmailed, ultimately, to those whose fingerprints
> match those on the knife.

Sure you can narrow it down. Max likelihood studies do it easily. The
Mau et al Monte Carlo study I've been citing apparently managed to deal
with 10 to the 40th trees, identifying 250 trees as comprising a 95%
credible zone (being posterior probabilities adding to 95%, amazing),
and 14 of which comprise 50% of probability. Now after this fine
mathmagic, I've the nerve to be annoyed that the tree of maximum
likelihood has a marginalized posterior probability of only .11.

> In systematics, we go out to collect
> evidence. A matrix is the result of our investigations. The
> probability of a result may be low in the face of no evidence, but is
> high in the context of the evidence. In fact, for the shortest tree,
> it is maximized, relative to the evidence.
> Ultimate probabilites for unique historical events (did they really
> happen?) are either 0 or 1.

Some might disagree. Depends on reference sets of similar events.

I suspect we agree more than disagree. Statistical evaluations have
major problems with assumptions and models. I am uncomfortable, however,
with imagining we can discover a pattern in nature with a method that
impresses a pattern (based on a simple model) on data, and saying that
the degree to which that pattern can be impressed on data is a measure
of the reconstruction of the pattern in nature. The degree to which the
pattern can be impressed on the data is NOT necessarily directly
apposite to the degree to which nature impressed its own pattern on the
data.

--

*******************************************************
Richard H. Zander, Buffalo Museum of Science
1020 Humboldt Pkwy, Buffalo, NY 14211 USA bryo at commtech.net
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