Friday, May 8, 2015

Jaynes: Probability (2003), ch. 3

While discussing the probability of drawing the same ball twice when sampling with replacement from an urn, Jaynes breaks off into a little "sermon" (pp. 64–66):
In probability theory there is a very clever trick for handling a problem that becomes too difficult. We just solve it anyway by:
  1. Making it still harder;
  2. Redefining what we mean by “solving” it, so that it becomes something we can do;
  3. Inventing a dignified and technical-sounding word to describe this procedure, which has the psychological effect of concealing the real nature of what we have done, and making it appear respectable.
In the case of sampling with replacement, we apply this strategy by
  1. Supposing that after tossing the ball in, we shake up the urn. However complicated the problem was initially, it now becomes many orders of magnitude more complicated, because the solution now depends on every detail of the precise way we shake it, in addition to all the factors mentioned above;
  2. Asserting that the shaking has somehow made all these details irrelevant, so that the problem reverts back to the simple one where the Bernoulli Urn Rule applies;
  3. Inventing the dignified-sounding word randomization to describe what we have done. This term is, evidently, a euphemism whose real meaning is: deliberately throwing away relevant information when it becomes too complicated for us to handle. (p. 64)
Just to be sure, he adds:
Shaking does not make the result “random,” because that term is basically meaningless as an attribute of the real world; it has no clear definition applicable in the real world. (p. 65)
I think I would agree with Jaynes that randomization in field experiments is akin to a protective ritual. To the extent that such a tirual is intended to protect us against a malicious Nature out to get us, it is absurd.

But like the proponents of randomized trials, Jaynes here fails to see that the evil adversary might in fact be a dishonest experimenter rather than a malicious Nature. Both of these characters are in principle vulnerable to strategies like randomization, but unlike Evil Nature, Evil Scientist actually exists.

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