The Wizard of Odds

After a truly debilitating holiday bacchanal last night, followed (almost immediately, it seemed) by a long day at work, I’m far too pooped to post. But I do have something interesting for you to read, if you like.

Anyone who pays attention to scientific and technological topics (or who reads the little messages generated by email spam filters) has probably heard of Bayes’ Theorem. If you’ve ever wondered what it was all about, you need wonder no more. Eliezer Yudkowsky has put together a wonderful essay about Reverend Thomas Bayes, “by far the most enigmatic figure in mathematical history”, and his marvelous theorem. Have a look here.

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2 Comments

  1. Kevin Kim says

    Fascinating article, but I’ll need to reread it several times before I truly grasp it. The most interesting aspect of the article was the deconstruction of Popper’s falsificationism, and the relegating of it to a “special case” in the larger Bayesian paradigm. Almost makes me wonder if that sort of move hints at infinite progression/regression: currents truths always subsumed into larger, more overarching truths, forever and ever, amen.

    Kevin

    Posted December 2, 2007 at 12:39 pm | Permalink
  2. Malcolm says

    The higher we climb, the more of the landscape we can see.

    But it’s important to put even the beautiful insights and generalizations offered by Bayesian analysis in perspective, and not get too carried away with the notion that Popperian falsifiability as the hallmark of science has now been superseded.

    Although Einstein’s generalization correctly extends Newtonian mechanics, it does so only in the last few decimal places, leaving Newton’s far simpler model perfectly adequate in almost all practical cases. In a similar way, the Bayesian insight here is that falsification of a scientific model depends upon correctly establishing the probability that a particular “falsifying” result is forbidden by the model. If you can manage to bump that up to 100% — that is to say, if you know that a given result is 100% guaranteed never to happen under your theory — then your theory is indeed falsified by such a result, even under the Bayesian paradigm.

    So the Popperian paradigm is the limiting case of the Bayesian one for low probabilities of exceptional results, just as the Newtonian paradigm is the limiting case of Einstein’s for low masses and velocities. When you are confident that result X is extremely unlikely under theory A, then an ocurrence of X falsifies A with high reliability indeed.

    Posted December 2, 2007 at 3:45 pm | Permalink