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On witnesses

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  • gentile_dave@emc.com
    Ron wrote: Let s consider a legal analogy. If witness A denigrates the character of witness B, do you believe witness A? No fair-minded person would do so
    Message 1 of 1 , Dec 12, 2007
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      Ron wrote:



      Let's consider a legal analogy. If witness A denigrates the character of
      witness B, do you believe witness A? No fair-minded person would do so
      without trying to find other evidence bearing on the case. And if there
      is
      no other evidence, the fair-minded person would surely be forced to
      suspend
      judgment, in other words, treat witness A's testimony as unreliable,
      that
      is, the testimony cannot be relied upon to be true.



      Dave:



      My approach would be to mentally adjust downward the probability that A
      was telling the truth and also adjust downward the probability that B
      was telling the truth. If witness A and B conflict, it lowers the
      probability of truth for both. I suppose one might argue about whether
      this is "fair", but from a strict information processing point of view,
      I believe it is correct.



      Digression on probability -



      Recently I've gained a little more insight into common perceptions of
      probability, so I'd like to elaborate on what I mean by "probability".
      In recent decades there have been two "camps" in statistics, a Bayesian
      camp, and a frequentist or traditional camp. My current approach
      incorporates elements of both. In a way it is analogous to the 3SH. I
      get the best of both competing camps, by introducing a change in
      assumptions. I find traditional statistics to be correct, but
      incomplete. I also disagree with the largest segment of the Bayesian
      camp, in that I don't think probability=personal belief. Rather I see it
      as an extension of logic from the deductive realm into the inductive
      realm.



      ''Degrees of belief are relative to a person and a time but not to
      evidence...Inductive probabilities are the opposite of this; they are
      relative to evidence but not to a person or a time.' Maher ([2006])



      Maher, P. [2006]: 'A Conception of Inductive Logic', Philosophy of
      Science, 73, pp. 513-23.



      But, moving away from my specific approach, one thing I've discovered is
      that for many probability=frequency. Dice or coins come to mind, where
      we know the limiting frequency. Thus when I say P=1/6th, I am making a
      statement of fact. It's an odd sort of fact, but still a fact. We are
      uncertain about the next outcome, but certain about the frequency.



      However, the more interesting questions, I believe, are when we are
      uncertain about the frequency as well. Here the probability is our best
      estimate of that frequency, (both Bayesians and frequentists can make
      this move). For Bayesians we are then dealing with "meta-probabilities"
      or probabilities of probabilities. I think not making this jump is what
      leads some outside the field to favor frequentist statistics, and not
      the Bayesian sort, whereas in reality this move is not something that
      can distinguish them. The camps will treat this move in different ways,
      but they can both make this move.



      That is a long way of getting at the point that if I say there is a 50%
      chance witness A is telling the truth, that is not mean that I think we
      know that 50% of the time the witness is truthful. Rather, given our
      ignorance of the frequency, this is the estimate of that frequency which
      minimizes our mean-square error.



      Probably too technical, and way off topic I suppose. But if anyone would
      like a copy of my paper (currently under review), I think I can share at
      this point.



      Dave Gentile

      Riverside, IL













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