I don’t blame the judges who made this present ruling; like most people today they are confused over the definition of probability and have got hung up over alleged differences in application of the concept to the past and the future. But if Bayes’ theorem is to be thrown out of court then it is time to use a rhetorical trick I have been advocating for some years. What you actually need in any problem involving uncertainty is a number representing how strongly one thing would imply another. More formally, the number i(A|B) is a measure of how strongly one binary proposition ‘B’ would, if true, imply the truth of a second binary proposition ‘A’, according t relations known between the referents of the two propositions. From the (Boolean) algebra of propositions it can be shown that the corresponding algebra of these numbers related to propositions is just the sum and product rules. On this basis I like to call the number “probability” but if anybody objects – traditionally frequentist statisticians, but today perhaps judges – then let’s call it something else (implicability?) and then we can use it and solve the problem anyway. As for Bayes’ theorem, don’t use the name if judges dislike it; just use the sum and product rules, from which it trivially follows.

In another recent case (that of Chris Huhne’s ex-wife) a jury was discharged after seeking clarification from the judge on what phrases like “reasonable doubt” meant. The judge refused to answer, and I have some sympathy with both sides of that exchange. This is all about the bolting of decision theory on to probability theory in order to come up with a verdict.

The appearance of Bayes in court in recent years has been driven mainly by DNA evidence. I regard this as a fleeting phase, because DNA testing will soon be so good as to identify people uniquely except in the case of identical twins.

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