You—Yes, You—Are Doing Probability & Statistics Wrong — Podcast

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Fellow users of probability, statistics, and computer “learning” algorithms, physics and social science modelers, big data wranglers, philosophers of science, epistemologists; other respected citizens. We’re doing it wrong.

Not completely wrong; not everywhere; not all the time; but far more often, far more pervasively, and in far more areas than you’d imagine.

What are we doing wrong? Probability, statistics, causality, modeling, deciding, communicating, uncertainty. Everything to do with evidence.

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  1. Heck. You can take the busy beaver function ( of (googolplex^googolplex). The busy beaver function provably grows incomputably fast. It grows faster than your towered exponentials or even an Ackerman function by an incomprehensibly huge margin. We’ll likely never know a decimal representation of the busy beaver function of even 7. Yet any finite number that can be defined, including the one that I just specified above, is smaller than almost every finite number. And all of those finite numbers are infinitely smaller than Aleph-0, the cardinality of the natural numbers.

    The cardinality of real numbers, the infinity of the continuum, is so large that, if a single number is drawn from the set of real numbers in the interval [0,1], the probability that it will be a rational number is 0 (well, more precisely, the rationals are a set of Lebesgue measure zero in that interval, the Lebesgue integral from 0 to one of the function “f(x)=1 for x rational, 0 for x irrational” yields 0). And the rationals are dense in the reals. And yet, the set I just named has the same cardinality as the set of points in all of R3 (the set consisting of the cartesian product of the (real numbers with the real numbers) with the real numbers.

    Amazing, philosophically fascinating, mind numbingly deep, I can get lost in time just contemplating (really, merely trying to grasp) it. You can discern that by the fact that I typed it out.

    But yet, so what? It’s like your harping on randomness. We all know that physical causes result in H or T in a coin flip. Of course H or T is “caused” each time the coin is flipped. Randomness simply means we can’t predict it at all. And we all know what we mean when we use the word.

    And of course theta (a parameter) is, in a regression, drawn from R1. And we’ll never know exactly which real number it is for a variety of reasons. But we can surely specify a bounded interval in which it lies. And we can calculate based on that (those) interval(s). And, if we understand the limits (the non delta epsilon kind of limits) of what we’ve done, it’s valid.

    And the infinite number of trials of the frequentist is also a red herring. It’s the inverse problem of the one posed by Berkeley in “The Analyst” wherein he describes Newton’s differentials as “ghosts of departed quantities.” But then, I wonder if you might not find Berkeley’s arguments compelling.

    I postulate that the casinos in Las Vegas or Macau weren’t built by people who were over certain.

  2. Briggs, how the heck are you religious? Evidence? You regularly post the works of St. Thomas Aquinas. You seem pretty secure in your understanding of physics. Evidence, like a math equation, is in the eye of the beholder. No one pretends to have literal certainty of a modeled abstraction, but many’s the time we poor mortal humans have manage to be right, and we’re not surprised.

    One more thing, you seem to be arguing for recklessness. Risk assessment only has the tools it has. To just be rid of that? Reckless thinking.


  3. “many’s the time we poor mortal humans have manage to be right, and we’re not surprised.”
    At least mark Carney admits the models aren’t all that.
    Anyone following the news the last week won’t be strutting confidence that ‘many’s the time’ models are right.
    That is laughable.

    JMJ religion and science are not at odds. There is more than one system of truth seeking. Evidence takes different forms. You keep mixing it up. Until you grasp this fact you will continue to mix it up. For “you” read anyone who thinks or likes to think science and religion are in conflict.

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