Re: [Synoptic-L] Bayesian statistics and salt
- At 08:55 PM 4/12/2006, E Bruce Brooks wrote:
>To: SynopticWell, you flat out declared, after quoting the problematic passage from
>In Response To: Bob Schacht
>On: The Persimmon Paradox
>BOB: Bruce, you're missing the point about Bayesian statistics. The
>philosophical issue here is: Is "truth" absolute, or is it relative?
>BRUCE: I don't know what "absolute truth" means, it sounds to me
>uncomfortably theological.. . .
>My response would be: No, it was wrong period.[snip]
>BOB: You take the side of absolute truth. This is all well and good, butBut you are not shy about responding "No, it was wrong period. "
>every day people make truth judgments without having all the facts. You do,
>too. David's just-so story was meant to illustrate this.
>BRUCE: Again, I am shy of the term "absolute truth." . . .
You can only declare it wrong on the basis of information not previously
known. At time A, it seemed right. But then at time B, you now declare it
"wrong period." So now what if I discover another piece of evidence that
shows you that it is probably right?
You modestly profess being shy about "absolute truth," but are not hesitant
to proclaim it.
So it again seems to me that you still do not understand the Bayesian process.
[Non-text portions of this message have been removed]
- To: Synoptic
In Response To: Bob Schacht
BOB: But you are not shy about responding "No, it was wrong period. " / You
can only declare it wrong on the basis of information not previously known.
At time A, it seemed right. But then at time B, you now declare it "wrong
period." So now what if I discover another piece of evidence that shows you
that it is probably right? / You modestly profess being shy about "absolute
truth," but are not hesitant to proclaim it.
BRUCE: I am shy about words like "absolute" and "truth" because they are all
too liable to be written in capital letters, and to get out of hand in an
ordinary secular argument. What I feel less shy about, in the present
example, is that the procedure offered in Dave's example is operationally
wrong, and so is every other statistical procedure applied to equally
inadequate data. I can find no merit in an answer being "right except not
corresponding to the truth." It merely means that the arithmetic was done
correctly. It doesn't mean that it was correct to do the arithmetic in the
Questions of who said what to who are rarely enlightening, but this one
happens to be both recent and on record. Let me in the interest of context,
and to get a little away from Truth questions, recapitulate Dave's
statement, and also my reply. Here goes:
DAVE (QUOTED BY ME): "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."
ME (IN RESPONSE): 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 . . . [the Persimmon Paradox followed, and was promptly
solved by Jeffery Hodges]
MY FURTHER COMMENT: I think it will be clear that my objection was (and I
herewith confirm that it remains) to using statistical methods, Bayesian or
other, when we don't have enough data, or the right data, to use them on.
This is a methodological objection. It is also categorical, in that it
applies to all use of statistics on insufficient data. Subject to
counterexamples, I don't concede that any statistical process, beginning
with insufficient data, can produce sufficient data, or can reliably reach
the same solution as it would have reached had sufficient (or appropriate)
data been available. If sufficient (or appropriate) data later become
available, the thing to do, in my opinion, is not to throw them into the
previous insufficient procedure, but to run a procedure on them de novo.
Don't spill milk on spilt milk.
It is open for any Bayesian here present to give an example of how operating
on an insufficient data set can produce a sufficient conclusion. This would
be a counter to my Persimmon example (to which I proceeded in the abridged
quote above), which tends to suggest that any operation on an insufficient
data set is invalid, and that any answer it may reach is in principle
perilous and in practice inactionable. My example is capable of
demonstration, at any desired length.
Failing such counterexample, I think my point stands. To me, it is useless
to say "Well, my answer would have been right if there had been enough data
to reach the right answer." The thing we need to know is when we *have*
enough data to reach the right answer, and the thing we need to do, in case
we do not have enough data, is not to calculate, but to refrain from
The infamous Literary Digest poll which mispredicted, by a landslide, the
outcome of the 1936 US Presidential election, was not "right on its
premises," that is meaningless. So is the proposition that the people who
ran that poll were nice people. It may well be true, but it's not relevant.
The poll was wrong on its assumptions; it was faulty as experiment design,
it was flawed from the outset, it was erroneous without extenuation. Its
wrongness is frequently expounded in elementary textbooks. It may have
"seemed right" to those who engineered it, but there is no content to that
rightness. It was and remains a mistake, in saecula saeculorum.
Statistics textbooks frequently give practice problems of an unreal sort,
whose effect is to accustom the statistic student to applying techniques to
unreal situations. I think the effect is bad. In the problem sets following
my lesson on the Poisson Distribution, I sometimes give the "textbook"
answers, just to practice using the tables, but I also attempt to show what
is wrong with the problems as there stated. I think this is a more helpful
approach. Apparently there are those in the math and engineering worlds who
think so too; at any rate, that page has been linked to by several
statistics classes in the academic sector, and queries about valid
application have been received from several engineers in the commercial
Be that as it may, I do not wish all this pother to obscure my initial
comment, which was that Dave Gentile's argument about the Markan "salt"
passages, insofar as it is based on the lexical and ritual facts, seems to
me well presented and worth considering. I am glad he put it online, and
hope he will get useful feedback from having done so. 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. I can't see how the attached Bayesian argument
enhances Dave's conclusions; to my mind, it threatens to disfigure them. Not
that I object to statistics, au contraire, but rather that I don't (so far)
find in this sort of data material on which statistics can fruitfully
E Bruce Brooks
Warring States Project
University of Massachusetts at Amherst
- 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