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Re: [Synoptic-L] Bayesian statistics and salt

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  • E Bruce Brooks
    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
    Message 1 of 9 , Apr 12, 2006
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      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
    • Horace Jeffery Hodges
      ... following five points: (1,2), (2,4), (3,6), (4,8), (5,8). Question: which of them is aberrant?
      Message 2 of 9 , Apr 12, 2006
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        E Bruce Brooks <ebbrooks@...> wrote:

        >>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, wouldn't the correct depend upon knowing more.
        Are these points on a larger curve, for instance? If
        the larger curve has a sort of bell shape, then all of
        these points might be non-aberrant.

        Or so it seems to this nonmathematician.

        Jeffery Hodges

        University Degrees:

        Ph.D., History, U.C. Berkeley
        (Doctoral Thesis: "Food as Synecdoche in John's Gospel and Gnostic Texts")
        M.A., History of Science, U.C. Berkeley
        B.A., English Language and Literature, Baylor University

        Email Address:

        jefferyhodges@...

        Blog:

        http://gypsyscholarship.blogspot.com/

        Office Address:

        Assistant Professor Horace Jeffery Hodges
        Department of English Language and Literature
        Korea University
        136-701 Anam-dong, Seongbuk-gu
        Seoul
        South Korea

        Home Address:

        Dr. Sun-Ae Hwang and Dr. Horace Jeffery Hodges
        Sehan Apt. 102-2302
        Sinnae-dong 795
        Jungrang-gu
        Seoul 131-770
        South Korea
      • Bob Schacht
        ... Bruce, you re missing the point about Bayesian statistics. The philosophical issue here is: Is truth absolute, or is it relative? You take the side of
        Message 3 of 9 , Apr 12, 2006
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          At 05:44 PM 4/12/2006, E Bruce Brooks wrote:

          >. . .I have looked at Dave's page
          >(<http://www.davegentile.com/synoptics/Mark.html),>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. . . .
          >
          >I can also locate the point on the page where I part company with its
          >learned author, . . .
          >
          >"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. . . .

          Bruce, you're missing the point about Bayesian statistics.
          The philosophical issue here is: Is "truth" absolute, or is it relative?
          You take the side of absolute truth. This is all well and good, but every
          day people make truth judgments without having all the facts. You do, too.
          David's just-so story was meant to illustrate this.

          The question that you have not come to grips with is this: How do you know
          when you have all the facts?
          That is why I've come to the conclusion that ALL of our conclusions must of
          necessity be viewed as tentative.

          In fact, I think that most Biblical scholars operate in somewhat of a
          bayesian fashion. However, this does not necessarily mean that I think
          David is right in his analysis, or that his use of bayesian statistics is
          correct.

          Bob





          [Non-text portions of this message have been removed]
        • E Bruce Brooks
          To: Synoptic In Response To: Jeffery Hodges On: Persimmon Paradox From: Bruce JEFFERY: Bruce, wouldn t the correct depend upon knowing more[?] BRUCE: My point
          Message 4 of 9 , Apr 12, 2006
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            To: Synoptic
            In Response To: Jeffery Hodges
            On: Persimmon Paradox
            From: Bruce

            JEFFERY: Bruce, wouldn't the correct depend upon knowing more[?]

            BRUCE: My point exactly. We cannot analyze or otherwise understand the data
            set until we know where it came from, or have enough further data to detect
            with some assurance the kind of situation it came from. The practical lesson
            I reach from this puzzle, which is not at all atypical of real-time,
            real-lab perplexities, is that applying statistics (or even human
            understanding) to such situations is not justified.

            E Bruce Brooks
            Warring States Project
            University of Massachusetts at Amherst
          • Horace Jeffery Hodges
            I m glad that this nonmathematician got it. Now, I just need to work on my grammar: Bruce, wouldn t the correct ANSWER depend upon knowing more[?] And I m
            Message 5 of 9 , Apr 12, 2006
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              I'm glad that this nonmathematician 'got it.' Now, I
              just need to work on my grammar:

              "Bruce, wouldn't the correct ANSWER depend upon
              knowing more[?]"

              And I'm supposed to know grammar...

              Jeffery


              --- E Bruce Brooks <ebbrooks@...> wrote:

              > To: Synoptic
              > In Response To: Jeffery Hodges
              > On: Persimmon Paradox
              > From: Bruce
              >
              > JEFFERY: Bruce, wouldn't the correct depend upon
              > knowing more[?]
              >
              > BRUCE: My point exactly. We cannot analyze or
              > otherwise understand the data
              > set until we know where it came from, or have enough
              > further data to detect
              > with some assurance the kind of situation it came
              > from. The practical lesson
              > I reach from this puzzle, which is not at all
              > atypical of real-time,
              > real-lab perplexities, is that applying statistics
              > (or even human
              > understanding) to such situations is not justified.
              >
              > E Bruce Brooks
              > Warring States Project
              > University of Massachusetts at Amherst
              >
              >
              >
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              University Degrees:

              Ph.D., History, U.C. Berkeley
              (Doctoral Thesis: "Food as Synecdoche in John's Gospel and Gnostic Texts")
              M.A., History of Science, U.C. Berkeley
              B.A., English Language and Literature, Baylor University

              Email Address:

              jefferyhodges@...

              Blog:

              http://gypsyscholarship.blogspot.com/

              Office Address:

              Assistant Professor Horace Jeffery Hodges
              Department of English Language and Literature
              Korea University
              136-701 Anam-dong, Seongbuk-gu
              Seoul
              South Korea

              Home Address:

              Dr. Sun-Ae Hwang and Dr. Horace Jeffery Hodges
              Sehan Apt. 102-2302
              Sinnae-dong 795
              Jungrang-gu
              Seoul 131-770
              South Korea
            • E Bruce Brooks
              To: Synoptic In Response To: Bob Schacht On: The Persimmon Paradox From: Bruce BOB: Bruce, you re missing the point about Bayesian statistics. The
              Message 6 of 9 , Apr 12, 2006
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                To: Synoptic
                In Response To: Bob Schacht
                On: The Persimmon Paradox
                From: Bruce

                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. Truth to me is absolute in the sense that it is
                not relative to my ideas of it; that it is "out there" and doesn't depend on
                my opinion of it, or on my thinking about it at all. If I kick a stone that
                I didn't suspect was there, it will still hurt. At least so Samuel Johnson
                has suggested, and I am content to adopt his conclusion as convincing.

                If I want to find out a particular truth (say, the vote in the 1946 Rumanian
                election, or the 1998 Guam election), I may have to put out an effort, and
                the election returns may have been selectively destroyed, or the election
                itself rigged, but these are merely complications. One of them, or one of a
                set including them, is what, to borrow a term from Ranke, really happened.

                I suspect that even Bayesian procedures aim to approach closer to "what is
                really so," and not merely to clarify, for internal purposes, "what I think
                is so." You can start out by thinking that all games of chance are even, but
                additional information (the insertion of additional information being the
                Bayesian trademark) will give you a better idea, not of the inside of your
                head, but of the odds of blackjack versus the odds of roulette. Certainly
                that was the view held by Mosteller in his conspicuously Bayesian analysis
                of the authorship of the Federalist Papers. He did not assume that the
                Federalist Papers were a figment of his imagination. He presented his
                Bayesian-derived conclusions as a better approximation to the facts of
                Federalist Papers authorship. At least in my edition of his book.

                Either Buddha predeceased Mahavira, or the reverse. Not both, not neither.
                The answer may be indeterminable, but it is not indeterminate. At the other
                end of the telescope, one of them happened.

                BOB: You take the side of absolute truth. This is all well and good, but
                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." The view I hold is that
                the situation is what it is (or was), regardless of how much we may know
                about it, or care about it, or conceive of it. In the absence of time or
                means to determine what the situation is, we often have to make best
                judgements and proceed on that basis. Sometimes we succeed, sometimes we
                don't. People differ in their ability to act on imperfect knowledge. (For
                that matter, be it noted, they also differ in their ability to act on
                perfect knowledge). The ones who are better at acting on imperfect knowledge
                tend to make better generals or (according to taste) text critics. That
                there exists an art of judging from imperfectly known facts raises, in
                principle, no questions about whether there *are* facts, and it involves no
                methodological issues about how to become better *acquainted* with the facts
                (the situation that is or was). I see no brief for Bayesian as opposed to
                Bernoullian (if that is the discussion we are having) in any of this.

                BOB: The question that you have not come to grips with is this: How do you
                know when you have all the facts?

                BRUCE: You never have all the facts; what you want is enough facts to base a
                reasonable conclusion on. How much is that? Statistically, at least in some
                situations, there are ways of determining that level; Neyman among others
                gave years of life to clarifying that type of question. If you argue from
                silence about the absence of a particular artifact type in a particular
                period, and additional excavations continue to be made, and if they turn up
                further examples of the known artifact types but no new types, then your
                conclusion is proportionately strengthened. More precisely, if you want to
                determine a proportion in a population, how large must your sample be? That
                is a fairly well researched and adequately answered question. If the
                population distribution is Poisson, for example, there is the Rule of Three,
                which holds that to determine with reasonable assurance (and the term
                "reasonable" is reasonably well defined in statistics) a proportion of 1/n
                in the population, you need to take a sample of 3n. Thus, if you want to
                establish a proportion of 1 in 1,000,000, you need to examine 3,000,000
                cases. That is not exact (it is more precisely x times the y of z), but it
                is close enough for practical purposes, and it is also easy to memorize. And
                so on.

                It is a piece of luck that, for samples of that size, Poisson closely
                approximates normal, so that the utility of the Rule of Three is wider than
                I may have implied in stating it. Engineers use a rough version of the Rule
                of Three all the time. Most of their bridges hold up pretty well.

                BOB: That is why I've come to the conclusion that ALL of our conclusions
                must of necessity be viewed as tentative.

                BRUCE: It is my impression that every responsible investigator, in physics
                as well as history, whether a Bayesian aficionado or not, reaches that same
                conclusion. The successful theory is the one which best accommodates the
                most data. Discovery of new data, or a better argument from the old data,
                will always displace the previous theory with a more adequate one. That is
                how science operates.

                Or almost always (people's emotions, including the emotions of
                scientifically trained people, continually clog up this particular
                equation).

                It seems to me that discussion like this one often blur two separate
                questions: (a) is there an empirical situation "out there," independent of
                my wishes or knowledge, and (b) if so, can I have adequate knowledge of that
                situation? For my money, the answer to (a) is Yes, and the answer to (b) is,
                It Depends. Depends on what? On what sort of situation it is, and how much
                knowledge is adequate for your purposes. The general who knows that the
                opposing force contains only 4,537 soldiers, whereas his contains 14,537,
                knows enough to make his next move. He doesn't need to know the names of the
                4,537 soldiers.

                Or, for that matter, of the 14,537, even though those names will in
                principle be available to him if needed. But his first thought on being
                offered that list, I imagine, would be to decline it, as hampering rather
                than assisting his thought processes. No?

                E Bruce Brooks
                Warring States Project
              • Bob Schacht
                ... Well, you flat out declared, after quoting the problematic passage from David s essay, ... [snip] ... But you are not shy about responding No, it was
                Message 7 of 9 , Apr 13, 2006
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                  At 08:55 PM 4/12/2006, E Bruce Brooks wrote:
                  >To: Synoptic
                  >In Response To: Bob Schacht
                  >On: The Persimmon Paradox
                  >From: Bruce
                  >
                  >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.. . .

                  Well, you flat out declared, after quoting the problematic passage from
                  David's essay,

                  >My response would be: No, it was wrong period.

                  [snip]


                  >BOB: You take the side of absolute truth. This is all well and good, but
                  >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." . . .

                  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.

                  So it again seems to me that you still do not understand the Bayesian process.

                  Bob



                  [Non-text portions of this message have been removed]
                • E Bruce Brooks
                  To: Synoptic In Response To: Bob Schacht On: Truth From: Bruce BOB: But you are not shy about responding No, it was wrong period. / You can only declare it
                  Message 8 of 9 , Apr 13, 2006
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                    To: Synoptic
                    In Response To: Bob Schacht
                    On: Truth
                    From: Bruce

                    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
                    first place.

                    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
                    calculating.

                    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
                    sector.

                    EMPHATIC CONCLUSION

                    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
                    operate.

                    Bruce

                    E Bruce Brooks
                    Warring States Project
                    University of Massachusetts at Amherst
                    http://www.umass.edu/wsp
                  • 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 9 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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