Striking a balance, weighting and Cladistics

[Richard Zander]

Tom:

Regarding probabilities of hypotheses, this is again a facet of the tedious
wrassling match between long-run frequency statisticians and Baysians, with
hypothesis testers grinning from the sidelines. See
   Gigerenzer, G., Z. Swijtink, T. Porter, L. Daston, J. Beatty & L. Krüger.
1989. The Empire of Chance. Cambridge Univ. Press, Cambridge.
for a nice critical review.

Carnap pointed out that there are two very different concepts of
probability.

Basically, long run frequency will give you a really good chance to predict
the future based on data collected over a long period of time and the
assumption that nothing will change (the data generation process continues
without hidden surprises). Popper pointed out that there is no assurance
that the data generation process will continue as before.

Bayesians use probability values for psychological expectation of single
instances, rolls of dice and so on. Although long-run frequentists point out
that one cannot really say what is going to happen in any one instance,
Bayesians profit in the long run by making their probablilistic judgements
on individual events though those individual events may differ in kind.

There is a lot of fire and argument, but really no problem. If you have lots
of information, you can predict things nicely with long-run frequency
techniques. If you have little information, or need to retrodict (postdict)
something that happened once in the past or will only happen once in the
future, use Bayesian methods.

There are also major differences in dealing with prior probabilities, in
that Bayesians, working with psychological expectation, include such priors,
but long-run frequentists SAY they don't but couch everything assuming no
other influences will obtain.

One major difference is that (in probability) long-run frequency allows one
to "win," say in a casino, with just a little more than 50% probability. But
Bayesians "win" (in probability) in a single throw of the dice only if the
probability (as psychological expectation) is very very high, and nearly a
sure thing.

WE are Bayesians, philosophically anyway, when we deal with phylogenetic
evolution.

R.

---------
From:
Richard H. Zander
Curator of Botany
Buffalo Museum of Science
1020 Humboldt Pkwy
Buffalo, NY 14211 USA
email: rzander at sciencebuff.org
voice: 716-896-5200 x 351



----- Original Message -----
From: "Thomas DiBenedetto" <TDibenedetto at DCCMC.ORG>
To: "'Richard Zander'" <rzander>; "Thomas DiBenedetto"
<TDibenedetto at DCCMC.ORG>; <TAXACOM at USOBI.ORG>
Sent: Tuesday, February 27, 2001 2:22 PM
Subject: RE: Striking a balance, weighting and Cladistics


> -----Original Message-----
> From: Richard Zander [mailto:rzander at sciencebuff.org]
>
> >My point is that there is no acceptable pattern in the data when the
> >analytic result is a bush or a weakly supported tree. One can find
> >"patterns" in totally random data.
>
> I agree with your point. There is obviously no acceptable pattern in a
bush,
> for there is no pattern represented. And a weakly supported tree should be
> labelled as such, and given as little credibility as it deserves.
> My only point on this issue was that I percieve these concerns to be
> recognized and addressed by most people in the field.
>
> >Note the the sum of the probabilities of poorly supported alternatives
may
> >be quite large.
>
> This seems in line with the points you make on your webpage (I've looked
at
> it but not had the chance to study it in detail). I have a question about
> your use of the Baysean concept of "probabilities of hypotheses". I note
> that you reference both Popper and Edwards on your webpage, and I seem to
> recall that both of them have thoroughly trashed the notion that
hypotheses
> (as opposed to events) can have probabilites attached to them. I havent
had
> the chance to think through this issue to the extent necessary, but I must
> admit that I find Poppers claim, that support or confidence in hypotheses
> cannot be squared with the probability calculus, to be compelling. I have
> always found the notion that one could measure the probability of a
> hypothesis being true to be a very bizarre concept, especially in
historical
> analyses. Edwards made the point by saying (paraphrase) - that one simply
> cannot view individual hypotheses as being drawn at random from some known
> distribution of hypotheses - as a way of building his argument that it is
> likelihood, not probability, that is the appropriate concept to use.
Having
> read these guys yourself, could you give me the outlines of the arguments
> against their position?
> -tom