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RE: [Synoptic-L] Bayesian statistics and salt

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  • Gentile, David
    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 subsequent thread. I
    Message 1 of 9 , Apr 13, 2006
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      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
      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
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