Tuesday, January 13, 2009

Philo’s Wager (or Why Bayesian reasoning is the Devil's logic)



"That's the devil's logic!"

Archdeacon to King's Chief Justice, Frollo
The Hunchback of Notre Dame (1939 script)
when Frollo admits his guilt, but says Esmeralda should hang anyway
since she used witchcraft to bewitch him




Bayesian reasoning is a variation of begging the question. It is mathematically "sound", but to what end?

Stephen Senn, Professor, Dept. of Statistics, University of Glasgow makes the following points:
The Myth of Objective Bayes

• Bayesian analysis cannot be a means of recovering the truth
• It is a means of recovering your truth
• What do you believe?
• This must be specified in your prior
• Remember it is impossible for another Bayesian to use your posterior distribution as input to his or her Bayesian analysis.
• He or she would be better off with a frequentist summary

(from "Is Ignoranace Bliss?" [PDF])

A generous attempt at reconciliation was made by David Freedman (1938–2008), who grew more wary of Bayesianism in his life:
My own experience suggests that neither decision-makers nor their statisticians do in fact have prior probabilities. A large part of Bayesian statistics is about what you would do if you had a prior. For the rest, statisticians make up priors that are mathematically convenient or attractive. Once used, priors become familiar; therefore, they come to be accepted as ‘natural’ and are liable to be used again; such priors may eventually generate their own technical literature … Similarly, a large part of [frequentist] statistics is about what you would do if you had a model; and all of us spend enormous amounts of energy finding out what would happen if the data kept pouring in. (Freedman, D.A., 1995)

Bayesian reasoning is popular with Christian apologists who attempt to put on a defense of "intelligent design" (see Brandon Fitelson's "Plantinga’s Probability Arguments Against Evolutionary Naturalism" [PDF]) or "Pascal's Wager" (see The Value of Life in Brownies and Milk in THE CONFABULUM). Then there is
"Philo"’s Wager

Choose atheism.

Argument: Atheism is the only rational belief, given that there is no evidence for God. And it seems reasonable to assume that if a rational god exists, then that god would only want rational people around him in Heaven. So only atheists (perhaps not all, there may be other considerations) will go to Heaven, if there is a heaven.


But it still remains, a la the archdeacon to Frollo:

      Bayesian reasoning is the Devil’s logic.


(see also Error and the Growth of Experimental Knowledge by Deborah G. Mayo, University of Chicago Press, 1996 [Google Books])


Update

Today: I discovered The Hunchback of Notre Dame (1939) will be on Turner Classic Movies this evening opposite the premiere of the 8th American Idol on FOX. (Pure happenstance. What were the odds?)

____________
From a rebuttal to my wager on THE CONFABULUM:


After all, your claim that there is “no evidence for God” is contradicted by the billions of people that believe that there is clear and reasonable evidence for God.


No comment.


It’s like a blind mind trying to claim that because he can’t see colors — he has no evidence for color! — that, ergo, color doesn’t exist.


Democritus (fragment 9, Sextus, adv. math. vii, 135):

"By convention there is sweet, by convention there is bitterness, by convention hot and cold, by convention color; but in reality there are only atoms and the void."