From: simon@dcs.warwick.ac.uk (Simon Clippingdale)
Subject: Re: In case Bales has convinced you of his honesty
Organization: Department of Computer Science, Warwick University, England
Date: Sat, 19 Dec 1992 18:06:08 GMT

In article <8002@tekig7.PEN.TEK.COM> bobb@tekig1.PEN.TEK.COM (Robert W Bales) writes:
>
> Simon  Clippingdale writes:
>> Your `dispute' with me is getting a little one-sided, in that I have now
>> issued no less than four invitations including my original followup (five
>> if you count this one) for you to respond to my allegation that you have
>> used statistics in a bogus manner

> I did not see the original followup.  I have seen at least most of the
> other invitations.
>
> I know I did not intentionally deceive.  I might have said something wrong.
> Or Simon could have misunderstood me.  By all means, post the response again
> and/or email it to me. [...]

OK, my original followup, erm, follows. I'll try to e-mail this article to
Mr. Bales as well. I'll be out of the lab and unable to read t.o. between
roughly 23 Dec and 4 Jan, so please e-mail me any responses as well as posting.


************************** begin quoted article *******************************

Newsgroups: talk.origins
From: simon@dcs.warwick.ac.uk (Simon Clippingdale)
Subject: Bob's Bogus Statistical Journey
Organization: Department of Computer Science, Warwick University, England
Date: Thu, 16 Jul 1992 17:49:39 GMT

This article is an attempt to point out the bogus statistical arguments
deployed in Bob Bales' post (Bob's comments indented with">").

In article <6110@tekig7.PEN.TEK.COM> bobb@tekig1.PEN.TEK.COM (Robert W Bales) writes:
>
>#  On the other hand, the standard theories of evolution
>#all predict that each and every vertebrate would share a common ancestor.
>#You can't say, well that's observed so it isn't a prediction, otherwise
>#there is no such thing as a successful prediction at any time.
>
> I'm not quite sure what Matt is saying in the second sentence.  A prediction
> is made before observations. (In this case, observations of vertabrates.)  A
> successful prediction is one which is confirmed by observations made after the
> prediction.

A "prediction" of a theory is *not* limited to one made prior to observations.
Logical consequences of a theory are also its predictions. Saying that a
theory "predicts X" means that X is a logical consequence if the theory is
correct, irrespective of whether or not X has already been observed.


>#If we are discussing whether specific forms of life would ever come into
>#existence this would be the case.
>
> When discussing the probability that evolution would produce what we see,
> we are discussing all possible outcomes of the evolutionary process.  These
> outcomes include specific forms of life either coming or not coming into
> existence.   So we *are* discussing this.

This is the crux of the statistical fallacy in Bob's post: "the probability
that evolution would produce what we see". This phrase is ambiguous, because
it can denote two different probabilities. These are:

(1) the conditional probability that, given what we see, evolution (rather
than something else) produced it

	P(E|D)   (E = evolution, D = observed data, | = "given")

and

(2) the conditional probability that, given that evolution happened, it would
produce what we see (rather than something else)

	P(D|E)

These two conditionals are connected by Bayes' Rule:

	P(X|Y)  =  P(Y|X) [P(X) / P(Y)]

and in general have different numerical values since the square-bracketed
term is not in general equal to unity.

The fallacy in Bob's post is to use (actually, imply) one where he should
use the other.

The question of interest to talk.origins is which of the two conditionals
P(E|D) and P(C|D) is the larger (C = "creation happened", E = "evolution
happened"). Bob incorrectly attributes his observations about P(D|E) and
P(D|C) to the vital P(E|D) and P(C|D).


>#However, by mentioning vertebrates in my original statement that you are
>#responding to, we have already agreed that vertebrates exist.  Thus, this
>#possibility is useless for further discussion.
>
> Not at all. When it comes to probabilities, possibilities that don't exist,
> but could have, are all important.  In Matt's first posting, he used the
> example of a "run" of continuous heads to compare the theories that the run
> was caused by a fair coin and that it was caused by a two-headed coin.  In
> this analogy, the possiblity that the fair coin could have come up tails was
> an important part of the analysis even though everyone agreed that tails had
> not existed in the example.
>
> Evolution, according to the theory, could have produced life without
> vertabrates. It didn't. Since evolution could have produced a result which
> doesn't exist, the probability of it producing the result which does exist 
> (which Matt has labeled p) is < 1.

What Bob is referring to here is P(D|E). It's actually a *lot* less than 1,
and indeed is bound to be miniscule, for the same reason that the probability
P(D|P) of a *particular* weather map D resulting at some given time from
climatic processes P is miniscule. There are a lot of possible weather maps
which P could have generated, and there are a lot of possible biotic outcomes
which evolution could have generated.

However, when he then says that "the probability of it [evo] producing the
result which does exist ... is < 1", he opens up the ambiguity mentioned
above: this could be misinterpreted as a statement about P(E|D) rather
than the statement about P(D|E) which it is.


> Note that since a Creator would not have had to produce vertabrates, the
> probability of creation producing vertabrates is < 1, also.

Right; that's P(D|C) there.


> The issue of DNA's possibly being required is not a red herring.  Since the
> only mechanism we see for storing gentic information is DNA, the theory that
> anything else is possible is only speculation.  If DNA is required, all
> theories are equally affected: all vertabrates produced by any means --
> creation, evolution, or whatever -- would have DNA.
>
> Suppose Matt were able to show that with DNA not required, creation has a
> vanishingly small probability. (I, of course, contend he has not done this.)

He could not reasonably be expected to. The importance of DNA is simply
that evolution predicts a mechanism for modifiable inheritance, while
creation does not. One is found. This can serve only to increase estimates
of P(E|D), not to show that P(C|D) is zero or nearly zero.

However, any increase in estimates of P(E|D) is bad news for creation
because it must tend to *reduce* estimates of P(C|D). Why? Because there
is only so much probability to go around: if X is the union of all
alternative explanations for D which are neither evolution nor creation,
then
	P(E|D) + P(C|D) + P(X|D) = 1.

Increases in estimates of P(E|D) must be accompanied by corresponding
decreases in the sum P(C|D) + P(X|D). If we acknowledge only evolution
and creation as possible explanations for D (i.e. we estimate that
P(X|D) = 0), then any increase in the running estimate of P(E|D) indeed
must come directly out of our estimate of P(C|D).

So a successful prediction of evolution, while not disproving creation,
must tend to *reduce* P(C|D).


> The possibility that DNA is required combined with the fact that the
> probability of creation is not vanishingly small in the latter case would be
> sufficient to show that "creation has a vanishly small probability" is not
> true in general.

Again, this is ambiguous. "Creation has a vanishly small probability"
looks like a statement about P(C), but may in the context of talk.origins
be assumed to be a statement about P(C|D).

In fact, in the discussion about whether or not DNA would be part of a
created system, Bob is talking about P(D|C), the probability that DNA
is observed (which is part of D) given that creation (C) happened.


> Thus, there are several ways in which evolution could have led to vertabrates
> with different means of storing genetic information.  Thus, as I said before,
> p < 1.

This, again, is P(D|E), *not* P(E|D).


>BB>But, as discussed  above, I contend that evolution does not require a
>BB>common means of storing genetic information, unless there is only one way
>BB>(DNA) to do so.
>
>#   This is false.  Evolution would predict that vertebrate life shares a
>#common ancestor.
>
> This is a conclusion formed *after* examining the evidence, not an a priori
> prediction.

See above - a prediction need not be a priori: it may also be a logical
consequence of the theory, and this is the sense in which Matt uses it here.


> If DNA is the only possible mechanism for carrying genetic information, any
> evolved or created vertabrates would necessarily have to use it.  If there are
> vertabrates, then the probability that either evolution or creation would
> produce them all with DNA is unity.
> 
> On the other hand, if there are other viable coding mechanisms, then a priori
> evolution, somewhere along the line, could have incorporated these, leading
> to vertabrates utalizing them.  The probabilitiy of either evolution or
> creation producing all vertabrates with DNA is, in each case, less than unity.
> It is unknown which has the higher probability.

Quite right. Note here that Bob is talking about P(D|E) and P(D|C), with
both being unity in the first paragraph and both being less than unity in
the second paragraph. But then he concludes with:


> Therefore, I disagree with Matt's statement that the probaility of evolution's
> producing the known results is greater than or equal to the probability of
> creation's producing them.

Back to the central ambiguity on which Bob is trading. The phrase "probability
of <process> producing <results>" is ambiguous.

Does he mean the probability of <process>, as opposed to some other <PROCESS>,
producing <results>, in which case that's P(<process>|<results>)?

Or does he mean the probability of <process> producing <results>, as opposed
to producing some other <RESULTS>, in which case that's P(<results>|<process>)?

He is implying in this last comment that he is comparing P(E|D) and P(C|D),
whereas in fact his whole argument has been about P(D|E) and P(D|C).

Related example of bogus use of a priori and a posteriori statistics,
courtesy DEA circa 1950:

	"98% of heroin addicts have previously used marijuana,
	 therefore marijuana use clearly leads to heroin addiction."

Now replace [using marijuana] with [drinking milk].

>   Bob Bales
>   Tektronix, Inc.

Cheers

Simon
-- 
Simon Clippingdale                simon@dcs.warwick.ac.uk
Department of Computer Science    Tel (+44) 203 523296
University of Warwick             FAX (+44) 203 525714
Coventry CV4 7AL, U.K.            or 0203 etc. if you're in the sunny UK


***************************** end quoted article ******************************

Christmas Cheer / Bah Humbug (delete as applicable)

Simon
-- 
Simon Clippingdale                simon@dcs.warwick.ac.uk
Department of Computer Science    Tel (+44) 203 523296
University of Warwick             FAX (+44) 203 525714
Coventry CV4 7AL, U.K.
Newsgroups: talk.origins