The Fallacious Confession


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One child is clearly a girl; the other is partially hidden by the family dog, so its gender is uncertain. What is the probability that the Smiths have two girls? Smith, who know that the child playing with the dog is William, would say that the probability of two girls is 0. So who is right? The answer depends on a choice of context. Have you sampled randomly from situations in which there are many different families in which either child plays with the dog? Or from families in which only one child ever plays with the dog?

Or are you looking only at a specific family, in which case probabilities are the wrong model altogether? The interpretation of statistical data requires an understanding of the mathematics of probability and the context in which it is being applied. Jeffreys of the University of Leicester and draws on a so-called variable number of tandem repeat VNTR regions in the human genome.

In each such region a particular DNA sequence is repeated many times. VNTR sequences are widely believed to identify individuals uniquely. For use in courts, scientists use standard techniques from molecular biology to look for matches between several different VNTR regions in two samples of DNA—one related to the crime, the other taken from the suspect.

Sufficiently many matches should provide overwhelming statistical evidence that both samples came from the same person. The source of the difference is, again, context. In the first case, the individual is conceptually being placed in a large population chosen for scientific convenience. In the second case, he or she is being placed in a less well defined but more relevant population—those people who might reasonably have committed the crime.

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The use of conditional probabilities in such circumstances is governed by a theorem credited to the Englishman Thomas Bayes. For example, in the case of the Smith children first scenario , we have. For the application to confessional evidence, Matthews designates. Matthews, has pointed out that a far more traditional source of evidence in court cases ought to be analyzed using probability theory—namely, confessions. Modern legal practice is quite skeptical about confessions known to have been obtained under duress.

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In the U. Suppose Mr. Smith tell you they have two children, one of whom is a girl. What is the probability that the other is a girl? Suppose that instead the Smiths tell you that their eldest child is a girl. What is the probability that the youngest is a girl, too? Probabilities of this type are said to be conditional, the probability of some event occurring given that some other event has definitely occurred. To see how subtle such issues are, suppose that one day you see the Smiths in their garden. One child is clearly a girl; the other is partially hidden by the family dog, so its gender is uncertain.


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What is the probability that the Smiths have two girls? Smith, who know that the child playing with the dog is William, would say that the probability of two girls is 0. So who is right?

The answer depends on a choice of context. Have you sampled randomly from situations in which there are many different families in which either child plays with the dog? Or from families in which only one child ever plays with the dog? Or are you looking only at a specific family, in which case probabilities are the wrong model altogether?

The interpretation of statistical data requires an understanding of the mathematics of probability and the context in which it is being applied. Jeffreys of the University of Leicester and draws on a so-called variable number of tandem repeat VNTR regions in the human genome.

The Fallacious Confession: A novel of oriental mystery

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