# Probabilities

Richard Zander bryo at COMMTECH.NET
Fri Dec 12 13:49:12 CST 1997

```Ted Schultz wrote:
>=20
> >Richard Zander wrote:
> >Not as such. One might view, however, subclades that are identical in
> >all trees with posterior probabilities that add to .5 or to, say, .95,
> >as the equivalent (the first for more evidence for than against, the
> >second to maybe actually call it a good estimation). Perhaps this woul=
d
> >not work, what do you think?
>=20
> I think you could do this in the same way as has been suggested for
> bootstrap confidence tree "clouds" (see below).  However, I don't think=
it
> would be fair to calculate this by giving equal prior probability to al=
l
> possible trees.

You can give equal prior probability to all trees and get just a few
with
decent posterior probabilities.=20
Mau, B., M. A. Newton & B. Larget. 1997. Bayesian phylogenetic inference
via Markov chain Monte Carolo methods. Mol. Biol. Evol. 14: 717=96724.
got 250 trees with posterior probabilities adding to .95, and eliminated=20
10^40 trees. I think they used equal prior probabilities, at any rate,
the paper is dense.

>=20

> These approaches are unlikely to satisfy you, however, because the 95% =
set
> of bootstrap trees is still a small subset of all possible trees, and y=
ou
> seem to want to calculate probability as a function of all possible tre=
es.

No no. The curve of probability density as a function of all possible
gives only a few trees any decent posterior probability. Don't know how
they do this. A sufficiently advanced phylogenetic analytic method is
indistinguishable from magic--A.C.Clarke, paraphrased.

>
> A comment: There is probably a compromise between affording all possibl=
e
> trees equal a priori probability vs. affording a single (most
> parsimonious/most likely) tree all of the posterior probability.  For
> instance, every character implies a tree.  Trees implied by a single
> character are usually largely unresolved when lots of taxa are involved.
> If only the resolved parts of these trees are considered, we could come=
up
> with a set of resolved trees (including all possibilities in subtrees w=
here
> no character affords resolution, or in which characters conflict about
> topology) that is implied by all the characters considered individually.
> Add to this subset all possible trees that can be generated by the
> Archie/Faith permutation method (which probably includes the first set;=
I'd
> have to think about that) and all trees that have ever been proposed by=
any
> taxonomist, and you will have a subset of all possible trees where,
> arguably, the majority of prior probability should reside.  Now perform
> analyses and let the data suggest how the probability should be distrib=
uted
> a posteriori.
>=20
> >Zander:
> >The frequentist statistical explanation is copasetic. So is the
> >Bayesian, but we must remember that we are assigning probabilities to
> >one event that happened in the past, one throw of the dice (worse, a
> >concatenated series of throws of the dice). So here we go with
> >statistical relevance again. An increase in probability does not
> >necessarily confer on a theory more evidence for than against. In
> >medicine, an increase in probability of disease is cause for concern b=
ut
> >I for one would like to see *real good* confidence in a null, not just
> >an increase in probability. How is your confidence measured?
> >
> I will readily agree with you that there are too many papers using scan=
ty
> (usually molecular) data to superficially "overturn" traditional system=
atic
> groupings.  However, one series of studies that comes to mind in which =
a
> group of researchers has recovered largely congruent phylogenies from
> morphology and multiple genes is represented most recently by Fang et a=
l.
> 1997.  Systematic Biology 46:269.  Regier, Mitter, Poole, and various g=
> students and postdocs have explored particular taxa and character syste=
ms
> deeply.  This contrasts markedly with the more common approach of using
> whatever genes (primers) are available, producing a study, and moving o=
n,
> and is much more likely to benefit phylogenetics in the long run.
>=20

Thanks for the fine review. I am illuminated but pleased in that we
agree on main points.

--=20

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

```