RE: [Synoptic-L] Bayesian statistics and salt
- Thank you very much for the response, and the favorable words.
I'd like to respond here to both this post and some issues raised on the
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.
Sr. Systems Engineer/Statistician
601 Oakmont Lane,
Westmont, IL 60559
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
Cc: Dave Gentile
On: Bayesian Salt
All that thought and work should not pass without comment, and so I
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
the argument from tradition and from established meanings of words and
usages of ritual, to be interesting and perhaps in the end convincing.
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
and I will certainly file it with my notes on this particular problem
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
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
wugs only come out at night, then we have omitted important information
will change our answer. Our first answer was not wrong; it was correct
its information set. And, with our new insight into the nocturnal
of snicky wugs, we now have a new correct probability for our new
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
general. In my view (not wholly unshared by elementary textbook
relevant information is omitted, or if irrelevant information is put
the statistical grinder, or if we attempt to use the wrong tool to open
right pecan, nothing good will ensue. Let me illustrate this by what I
call (borrowing a term from another list where I raised this same
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?
E Bruce Brooks
Warring States Project
University of Massachusetts at Amherst