Loading ...
Sorry, an error occurred while loading the content.

Re: [Synoptic-L] Bayesian statistics and salt

Expand Messages
  • 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 1 of 9 , Apr 12, 2006
    • 0 Attachment
      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 2 of 9 , Apr 12, 2006
      • 0 Attachment
        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 3 of 9 , Apr 12, 2006
        • 0 Attachment
          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
          >
          >
          >
          > ------------------------ Yahoo! Groups Sponsor
          > --------------------~-->
          > Join modern day disciples reach the disfigured and
          > poor with hope and healing
          >
          http://us.click.yahoo.com/B6T8nB/Vp3LAA/EcBKAA/J2VolB/TM
          >
          --------------------------------------------------------------------~->
          >
          >
          > Synoptic-L homepage: http://NTGateway.com/synoptic-l
          >
          > Yahoo! Groups Links
          >
          >
          > Synoptic-unsubscribe@yahoogroups.com
          >
          >
          >
          >
          >
          >


          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 4 of 9 , Apr 12, 2006
          • 0 Attachment
            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 5 of 9 , Apr 13, 2006
            • 0 Attachment
              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 6 of 9 , Apr 13, 2006
              • 0 Attachment
                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 7 of 9 , Apr 13, 2006
                • 0 Attachment
                  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
                Your message has been successfully submitted and would be delivered to recipients shortly.