topic.

Here is a nice powerpoint presentation of the history.

http://www.fnal.gov/orgs/gsa/calendar/np/2005/talks/ProbabilityHistory.ppt

It even talks about Pascal's wager, but it leaves off before the present

day.

Here is an Amazon link to the book

http://www.amazon.com/gp/product/0521592712/qid=1141485882/sr=2-1/ref=pd_bbs_b_2_1/002-8906425-0680820?s=books&v=glance&n=283155

Reading Jaynes is reading a polemic. He died before the book was published,

and was a voice in the wilderness for a long time.

There is indeed a revolution in progress, but it is still going on and

there are two camps. Frequentists tend to be pure math types. The concern is

over some details of how exactly it is grounded in mathematical axioms.

Given that I don't think mathematics can say what its exact grounding really

is, I'm not overly concerned. To me Bayesian has a firm philosophical

foundation, and mathematics has problems with its philosophical foundation.

Most things that can be done with Bayesian statistics can be done by the

frequentist, but not all things, and no one denies that the extra things

that Bayesian can do are useful. As computers and information theory become

more and more important, it seems er...probable that Bayesian will continue

to grow in importance. Many books now mention only in passing that there is

a philosophical issue, and get on with telling you how to use it for

business or science, or whatever.

In that 6 horse race, when the horses have never run, the frequentist has no

answer, but the Bayesian has an answer of 1/6th. Frequentists see an

external "real" probability, that they are estimating. Bayesian is all

about an internal probability, *given the information available*. For the

Bayesian 1/6th is not an estimate. It is the right answer given his current

information. And that is as right of an answer as is possible at that point.

Sure we really want the best answer given all the information, but the best

we can ever get is the best answer given the information we have. That is

the Bayesian answer.

For our purposes here, however, since we are not actually doing

calculations, the distinction between Bayesian and frequentist is important,

since it involves how we understanding what we are doing. It could be taught

to humanities students without math. I did a finance class involving it that

did very little math. It was about understanding simple everyday questions

that you needed to "think Bayesian" for, to get the right answer. I should

really talk to that professor to get a copy of his questions. What I

observed however is that some people (myself and one other student) got it

before being taught, because we have always thought that way. A few more

slowly got better at it, but half the graduate class still did not get it

after 11 weeks.

So, that may indeed make it a tough sell. But there is really no way to

"convert" to frequestist here, since the concept is the issue. It's not

actually identical with eisegesis, but close enough for the issue here.

Bayesian statistics would say that between arguments that use eisegesis the

one that brings the most data to bare on the question most effectively will

be the best answer. I've convinced myself that I agree its a bad idea for

most of this area of study. Not because there is anything wrong with the

application of Bayesian thinking here, in theory its still the best method,

but as a practical matter with little data and strong opinions, it is a bad

choice. But I also am convinced its the right, and really the only approach

that gets the right answer for "salt" in Mark.

Anyway, I have some reading to do. But, again, thanks for the response. It

is appreciated.

Dave Gentile

Riverside, IL

----- Original Message -----

From: "E Bruce Brooks" <ebbrooks@...>

To: "David Gentile" <GentDave@...>; "Synoptic"

<synoptic@yahoogroups.com>

Sent: Saturday, March 04, 2006 2:06 AM

Subject: Re: [Synoptic-L] When eisegesis is apphorpriate

> To: Synoptic

> In Response To: Dave Gentile

> From: Bruce

>

> Dave has been advocating Bayesian probability without on-list response. I

> have no informed response to offer. But in the thought that something is

> more courteous than nothing, as a list reply to a sincerely urged list

> proposal, I venture to post this *uninformed* response.

>

> 1. Dave is not just advocating statistics, he is advocating Bayesian

> statistics.

>

> 2. Dave asked if Biblical [sic, please] students were exposed to Bayesian

> probability. I don't know. My guess would be that no student of the

> humanities is exposed to probability, Bayesian or other, and that the

> whole

> idea of probability, or of calculations in any form whatever, is anathema

> to

> these fields.

>

> 3. I suspect that Dave is right, and that especially in certain fields

> (archaeology being one about which I have some information), Bayesian

> probability is the "gold standard" for interpretation. See however next.

>

> 4. A revolution may have occurred without my being notified, but last I

> checked, Bayesian probability was controversial among statisticians

> generally. My impression is that the issue Dave most recently addressed,

> that is, the assigning of "prior probabilities" to options of occurrence,

> these to be then refined in the light of later knowledge, is the usual

> sticking point. If we are betting on a six-horse race (and since the

> classic

> days of Jimmy Savage, betting is the basic Bayesian paradigm), and if, as

> novices, we have no reason to choose one horse over another, we may

> reasonably assign equal probabilities to the event of each of the six

> horses

> winning the race. We then pick one at random, and put down our money. This

> is called "distributing the ignorance." If, however, unbeknownst to us,

> five

> of the horses are broken-down old farm nags, and the sixth is a trained

> thoroughbred in the prime of vigor, the probabilities are not in fact

> equal,

> but heavily favor Horse Six. The notion that probabilities of occurrence

> are

> not in our heads, but are "out there" in real space and time, is called

> the

> "frequentist" position. The frequentist position has its distinguished

> advocates, and last I heard, it even has its own professional association,

> the Bernoulli Society, quite separate from that of the Bayesians, to keep

> tempers down, and to prevent irresolvable arguments arising over lunch.

>

> 5. I haven't read Jaynes (and if he is the same guy who wrote the book on

> the Bicameral Mind, I am not going to be in a hurry to). But I do note the

> difficulty of presenting a statistical argument to a lay public in

> Bayesian

> form. How much, say the classic Bayesians, are you willing to bet on this?

> (Jimmy Savage wrote a whole book on games of chance). Well, myself for

> one,

> and perhaps not a few seminarians for two and three, will bear in mind

> certain maternal cautions from tender years, and say, "I am not willing to

> bet anything whatever, under any circumstances." Or pick up hitchhikers.

> Or

> or or.

>

> Here, perhaps, is the difficulty. (The dubious repute of "eisegesis" in

> Biblical studies, as reported by Dave, may indeed be a parallel of sorts).

>

>

> 6. It need not be thought that Bayesian methods are the only path to the

> answers they purport to reach. During the height of the Bayesian

> enthusiasm

> as it affected what I have called the humanities (and this was a good few

> decades ago), Fred Mosteller wrote a book on distinguishing authorship

> within the Federalist Papers. He offered the book not as a revelation (the

> answer is known; Madison's authorship list is correct), but as an example

> of

> the power of Bayesian methods. I was able to take up that problem de novo,

> with frequentist rather than Bayesian methods, and achieve a power of

> discrimination superior to that demonstrated by the much more complex

> calculations used by Mosteller. Given that experience, my suspicion is

> that

> any nontrivial and valid Bayesian result can also be reached by, and

> stated

> in terms of, frequentist assumptions. If so, I would suggest that a

> frequentist exposition of the result (however it was originally reached)

> may

> be better for wide audience situations. Frequentist assumptions are

> intuitively more natural than Bayesian ones.

>

> Let it be recalled also that Bayes himself had doubts about the validity

> of

> his formula, and did not himself publish his result, it was done

> posthumously and by another hand. Might not a true Bayesian take the

> historical Thomas Bayes as a model, and be reticent as to whether Bayesian

> is the One True Way to do statistics?

>

> 7. So my practical question for Dave would be: Can the argument be stated

> in

> frequentist terms? Or is it irretrievably bound up with the Bayesian

> paradigm? If the latter, I could not myself avoid having a priori doubts

> (pun intended) about its efficacy.

>

> With best wishes to Dave and all other numerate persons,

>

> Bruce

>

> E Bruce Brooks

> Research Professor of Chinese

> Warring States Project

> University of Massachusetts at Amherst

> http://www.umass.edu/wsp

> [profiles of Bayes, Savage, and Mosteller are in the Statistics section]

>