corroboration

[R. Zander]

Bengt Oxelman wrote:

> >Example: Suppose you have two suspects in a criminal investigation. Th=
ere are
> >two witnesses who say Suspect A did it, and one that says Suspect B di=
d it.
> >Suppose the number of witnesses is directly proportional to evidence o=
f guilt.
> >Do we hang Suspect A? Remember that Suspect A has minimum falsifiabili=
ty
> >(easier to falsify evidence against Suspect B), maximum likelihood (2 =
out of 3
> >witnesses), maximum parsimony (simplest hypothesis), and maximum poste=
rior
> >probability (2/3)\(2/3 + 1/3) =3D .66. Of course we don't hang him. No=
w suppose
> >we have more witnesses, 2 more that say he did it and 1 more that says=
, no,
> >Suspect B did it. Again the optimum hypothesis is that Suspect A did i=
t and
> >optima from both data sets are the same! But there is no real change i=
n
> >probability, since the additional evidence against A is accompanied by
> >additional evidence against B. There is no corroboration by two or mor=
e data
> >sets given the same "best" hypothesis when evidence remains contradict=
ory.
> >This
> >is the case in most phylogenetic analyses.
>
> There are alternative views on probabilities here. Let us just imagine =
that
> we have a box with 1000 balls, black or white. We want to know if there=
 are
> more black balls than white. First we draw 3 balls at random, and get t=
wo
> black and one white. Then, we draw three more, again two black and one
> white. Has the probability that the box contain more black balls than w=
hite
> increased?

The probability that it contains more black balls than one ones will quic=
kly be
established, but there is no contradictory data in your example about thi=
s.

In your example, additional samples increases your accuracy in estimating=
 the ratio
of different balls. This is a statistically consistent method and the dat=
a
eventually converges to the correct solution.

But in evolutionary studies, if a black ball supports one hypothesis and =
a white
ball supports a second one, then we get, after much sampling (after many =
data sets
are examined) a mixture of balls--a set of contradictions that does not c=
hange.
Thus, optimal solutions that reappear with new data sets do not themselve=
s increase
the probability of the optimal solution.


> Yes! And this is how resampling statistics (bootstrap,
> jackknife) in cladistics could (and should?) be viewed. Assuming that t=
he
> characters at hand are drawn by random from the universe of characters,=
 the
> 'p' value is the probability that a given subgroup (topology or whateve=
r)
> will be found in another independent character sample of the same size.

Not if the characters are contradictory. Only if the ratio of characters =
supporting
a hypothesis change in a new data set can there be changes in the probabi=
lity of
one hypothesis versus another. This is how analysis of total evidence mus=
t work.

> Forgive me for being at loss about the exact philosophical meaning of
> 'corroboration', but I think it is nonsense to say that finding another
> character set with congruent pattern does not strengthen the hypothesis
> generated by the the first characters.

Then we must agree to disagree. I appreciate your comments, Bengt.


>
>
> Bengt Oxelman
>
> Dept. of Systematic Botany, Stockholm University
> Lilla Frescativ=E4gen 5, S106 91 Stockholm
> Sweden
>
> Phone: +46 8 161215
> Fax:   +46 8 165525
> Internet e-mail: bengt.oxelman at botan.su.se



--


Richard H. Zander
Curator of Botany, Buffalo Museum of Science
1020 Humboldt Pkwy, Buffalo, NY 14211 USA
bryo at paradox.net   voice: 716-896-5200 ext. 351