richard_dawkins_-_the_god_delusion

106 T H E G O D D E I, U S I O N
hypothetical murder as his test case to demonstrate Bayes'
Theorem. The detective marshals the evidence. The fingerprints on
the revolver point to Mrs Peacock. Quantify that suspicion by
slapping a numerical likelihood on her. However, Professor Plum
had a motive to frame her. Reduce the suspicion of Mrs Peacock by
a corresponding numerical value. The forensic evidence suggests a
70 per cent likelihood that the revolver was fired accurately from
a long distance, which argues for a culprit with military training.
Quantify our raised suspicion of Colonel Mustard. The Reverend
Green has the most plausible motive for murder.* Increase our
numerical assessment of his likelihood. But the long blond hair on
the victim's jacket could only belong to Miss Scarlet. . . and so on.
A mix of more or less subjectively judged likelihoods churns around
in the detective's mind, pulling him in different directions. Bayes'
Theorem is supposed to help him to a conclusion. It is a mathematical
engine for combining many estimated likelihoods and
coming up with a final verdict, which bears its own quantitative
estimate of likelihood. But of course that final estimate can only be
as good as the original numbers fed in. These are usually
subjectively judged, with all the doubts that inevitably flow from
that. The GIGO principle (Garbage In, Garbage Out) is applicable
here - and, in the case of Unwin's God example, applicable is too
mild a word.
Unwin is a risk management consultant who carries a torch for
Bayesian inference, as against rival statistical methods. He
illustrates Bayes' Theorem by taking on, not a murder, but the
biggest test case of all, the existence of God. The plan is to start
with complete uncertainty, which he chooses to quantify by assigning
the existence and non-existence of God a 50 per cent starting
likelihood each. Then he lists six facts that might bear on the
matter, puts a numerical weighting on each, feeds the six numbers
into the engine of Bayes' Theorem and sees what number pops out.
The trouble is that (to repeat) the six weightings are not measured
quantities but simply Stephen Unwin's own personal judgements,
turned into numbers for the sake of the exercise. The six facts are:
* The Reverend Green is the character's name in the versions of Cluedo sold in
Britain (where the game originated), Australia, New Zealand, India and all other
English-speaking areas except North America, where he suddenly becomes Mr
Green. What is that all about?