Thursday, July 19, 2007

Oh Joy, Another 'Copernican Principle' Post

by Tom Bozzo

As a follow-up from the earlier post on the topic, in the Crooked Timber thread following Quiggin's post, commenter RB points to a letter to Nature's editor from 1994 by Johns Hopkins biostatistician Steven Goodman making the case that Gott's reasoning is an example of an old statistical fallacy. (Goodman posted it as a comment to Tierney's NYT blog.) Goodman's general thrust — 'lies, damn lies, statistics' — is correct, but he maybe goes a bit too far in deploying the f-word.
Simply put, the principle of indifference [i.e., the fallacy] says that it you know nothing about a specified number of possible outcomes, you can assign them equal probability. This is exactly what Dr. Gott does when he assigns a probability of 2.5% to each of the 40 segments of a hypothetical lifetime. There are many problems with this seductively simple logic. The most fundamental one is that, as Keynes said, this procedure creates knowledge (specific probability statements) out of complete ignorance.
Actually, there is a more charitable version than this, which is how I'd previously set up the problem, and how Monton and Kierland characterize Gott's original argument. In my account, the uniform distribution of the observation point is explicitly part of the (assumed) information set; I've packed my free lunch as it were. If that doesn't sound like much, it's not. However, I would submit that the more useful thing to argue over is whether the uniform distribution assumption is warranted. As it happens, I said before that the assumption is strong before, and what I mean is that in practice it seems unwarranted for the array of amusing social applications that Gott can't seem to resist.

But for a little more damnation by faint praise, let's just remember what's being promised by the method: a prediction within a factor of 39 of the start-to-present interval. As a practical matter, the real problem in many cases is not that too much fabricated information is being brought to bear, especially at the upper bound.

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