Re: Fuzzy logic ,minds and Bayes

From: P.G.Hamer (pgh@nortelnetworks.com)
Date: Fri Feb 02 2001 - 18:40:38 MET

  • Next message: nicholas@esit.com: "Learning Mechanism"

    Martin Lefley wrote:

    > Surely
    > accurate Bayesian reasoning needs complete conditional data distributions,
    > this is never available and I believe if it is, this applies complete data,
    > in which case any learning system could reason consistently, accurately
    > perfectly.

    I don't think so. Consistency requires a logic which derives exactly the same
    result irrespective of the chain of logic/calculation by which it was derived.

    As Cox has pointed out, the combination rules of statistics may be unique
    in this respect.

    However -- even if this is true -- it may not be of any significant practical
    import. [And I speak as a statistically inclined lurker.]

    Firstly. How big are the inconsistencies for `reasonably' long chains
    of derivation.

    Secondly. Most floating point systems are formally inconsistent, as
    truncation, rounding, under/overflow, etc. may be different for different
    ways of ordering the same arithmetic calculation. Mostly this doesn't
    matter too much. Sometimes (as numerical analysts know only too well)
    it can be important and steps have to be taken to minimise its impact.
    [This may be as simple as evaluating (a+b)(a-b) rather than a^2-b^2.
    Or as complex as requiring a full analysis of the propagation of truncation
    errors.]

    Basically `all models are wrong'. So worrying if you have an infinite
    number of significant digits in your calculated answer should not be
    your biggest concern.

    As so often, we have a black and white formal characterisation. With all
    sorts of real-world grays in between.

    Peter

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