I'd like to respond here to both this post and some issues raised on the

subsequent thread.

I think Bayesian analysis is agnostic about the existence of absolute

truth, but if absolute truth does exist, in Bayesian analysis, you need

infinite/all possible information to arrive at it. Only if you can

eliminate the possibility that additional information exists, can 100%

certainty be achieved. So all knowledge is indeed tentative, as far as

Bayesian analysis is concerned.

Addressing the issue of doing statistics with inadequate or

inappropriate inputs -

An analogy may be helpful here. What axioms are to deductive logic, the

information set is to Bayesian analysis. A deductive argument may be

completely sound, but it is only as good at approximation of "truth" as

its axioms. In Bayesian analysis if the math is done correctly, the

answer is only as good as the information fed into it. So when I say

"Our first answer was not wrong; it was correct for its information

set." I mean that in the much the same way that a deductive argument can

be sound but counter to our best estimate of reality.

So I would maintain that when the math is done correctly a Bayesian

answer is correct for its information set. Whether or not a Bayesian

answer is useful for practical implementation in a given situation can

depend on other factors. For example, if we have used all the

information available to us, but we strongly suspect others have

important additional information, it may be unwise to proceed based on

our answer i.e. if we write a program that is good a making money based

on market patterns, we might want to use it, but we don't want to use it

to bet against insider trading.

So in critical analysis of a deductive argument one wants to examine the

assumptions or axioms. In critical analysis of a Bayesian argument we

want to look for important information that was omitted. For my salt

argument, I believe I've made appropriate use of the information at my

disposable, but of course, I may be uninformed on some key point.

Is Bayesian statistics appropriate here? I think you are right when you

say "I suspect that in the end, like any other proposal of its type, it

will stand or fall on how well it addresses the lexical and ritual

facts, as well as on what facts others may cite which it does not

address, or what possibilities others may propose which it did not

envision." All the Bayesian analysis does is add a bit of rigor to the

thought process, and give a quantitative answer associated with the

result. (Which is only as valid as its information set).

I think having such a number could be useful. In New Testament studies,

at least it seems to me, things that only seem to be established at say

70% probable are cited as near fact, and things that seem highly

probable say at the 99.9% level are routinely questioned. At least that

is my subjective observation. Having some sort of quantitative estimate

of the certainty of conclusion, even if such quantities are estimates

subject to revision, would seem to be useful, at least to me.

Thank you again for the response.

Dave Gentile

Sr. Systems Engineer/Statistician

EMC Captiva

EMC Corporation

601 Oakmont Lane,

Westmont, IL 60559

P: 630-321-2985

F: 630-654-1607

E: Gentile_Dave@...

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

From: E Bruce Brooks [mailto:ebbrooks@...]

Sent: Wednesday, April 12, 2006 10:44 PM

To: Synoptic@yahoogroups.com; Gentile, David

Subject: Re: [Synoptic-L] Bayesian statistics and salt

To: Synoptic

Cc: Dave Gentile

On: Bayesian Salt

From: Bruce

All that thought and work should not pass without comment, and so I

venture

to make a comment, if only to satisfy my Chinese notions of propriety.

I have looked at Dave's page

(http://www.davegentile.com/synoptics/Mark.html), and find the first

part,

the argument from tradition and from established meanings of words and

usages of ritual, to be interesting and perhaps in the end convincing.

On

the last point I am personally holding out for the moment, but as a

commentary, the argument seems to me to have merit. I am glad Dave did

it,

and I will certainly file it with my notes on this particular problem

area

of Mark, and continue to ponder it.

I can also locate the point on the page where I part company with its

learned author, and perhaps not surprisingly it is the methodological

part.

I find myself losing it at about the following paragraph:

"On the other hand, a quite legitimate criticism of a Bayesian result is

that important information, that is known, was not considered that would

effect the outcome. For example, if we know it is daylight, and that

snicky

wugs only come out at night, then we have omitted important information

that

will change our answer. Our first answer was not wrong; it was correct

for

its information set. And, with our new insight into the nocturnal

behavior

of snicky wugs, we now have a new correct probability for our new

information set."

My response would be: No, it was wrong period. I don't see this as

exclusively an objection to Bayesian, it is a caution about statistics

in

general. In my view (not wholly unshared by elementary textbook

writers), if

relevant information is omitted, or if irrelevant information is put

into

the statistical grinder, or if we attempt to use the wrong tool to open

the

right pecan, nothing good will ensue. Let me illustrate this by what I

will

call (borrowing a term from another list where I raised this same

question)

the Persimmon Paradox:

Take or make a sheet of graph paper, and plot the following five points:

(1,2), (2,4), (3,6), (4,8), (5,8). Question: which of them is aberrant?

Bruce

E Bruce Brooks

Warring States Project

University of Massachusetts at Amherst