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The Inexpert Witness

The Inexpert Witness. Born 1933 Distinguished paediatrician Famous for “Munchausen Syndrome by Proxy” Expert witness in cases of suspected child abuse and murder Notorious for high-profile miscarriage of justice in Sally Clark trial. The Case of Sally Clark.

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The Inexpert Witness

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  1. The Inexpert Witness • Born 1933 • Distinguished paediatrician • Famous for “Munchausen Syndrome by Proxy” • Expert witness in cases of suspected child abuse and murder • Notorious for high-profile miscarriage of justice in Sally Clark trial

  2. The Case of Sally Clark • Solicitor Sally Clark was tried in 1999 for the murder of two children (Christopher, 11 weeks), (Harry, 8 weeks). • Medical testimony divided • Meadow’s evidence was decisive, but flawed. • Appeal in autumn 2000 was dismissed • Second appeal (for different reasons) in 2003, but ruling cast doubt also on Meadow’s testimony; Clark released. • Sally Clark died on16 March 2007 of alcohol poisoning

  3. Publish and be damned • This case was mentioned in my book “From Cosmos to Chaos” • In 2005, Meadow appeared before a GMC tribunal and was struck off • He appealed and pending the outcome my book was shelved by OUP • His appeal succeeded, but was guilty of “serious professional misconduct” so it was published.

  4. The Argument • The frequency of natural cot-deaths (SIDS) in affluent non-smoking families is about 1 in 8500. • Meadows argued that the probability of two such deaths in one family is this squared, or about 1 in 73,000,000. • This was widely interpreted as meaning that these were the odds against Clark being innocent of murder. • The Royal Statistical Society in 2001 issued a press release that summed up the two major flaws in Meadow’s argument.

  5. Independence • There is strong evidence that the SIDS does have genetic or environmental factors that may correlate within a family • P(second death|first)=1/77, not 1 in 8500. • Changes the odds significantly unless X and Y are independent

  6. The Prosecutor’s Fallacy • Even if the probability calculation were right, it is the wrong probability. • P(Murder|Evidence) is not the same as P(Evidence|Murder), although ordinary language can confuse the two. • E.g. suppose a DNA sequence occurs in 1 in 10,000 people. Does this mean that if a suspect’s DNA matches that found at a crime scene,the probability he is guilty is 10,000:1? • No! • E.g. in a city of a million people, there will be about 100 other matches. In the absence of any other evidence, the DNA gives of odds of 100:1 against the suspect being guilty.

  7. Inverse Reasoning • If we calculate P(Deaths|SIDS) to be very small, that does not necessarily mean that P(Murder|Deaths) has to be close to unity! • We need to invert the reasoning to produce P(SIDS|Deaths) and P(Murder|Deaths) both of which are small! • The only fully consistent way to do this is by Bayes’ Theorem, although a (frequentist) likelihood ratio would also do…

  8. A Load of Balls… • Two urns A and B. • A has 999 white balls and 1 black one; B has 1 white balls and 999 black ones. • P(white| urn A) = .999, etc. • Now shuffle the two urns, and pull out a ball from one of them. Suppose it is white. What is the probability it came from urn A? • P(Urn A| white) requires “inverse” reasoning: Bayes’ Theorem

  9. Urn A Urn B 999 white 1 black 999 black 1 white P(white ball | urn is A)=0.999, etc

  10. Bayes’ Theorem: Inverse reasoning • Rev. Thomas Bayes (1702-1761) • Never published any papers during his lifetime • The general form of Bayes’ theorem was actually given later (by Laplace).

  11. Bayes’ Theorem • In the toy example, X is “the urn is A” and Y is “the ball is white”. • Everything is calculable, and the required posterior probability is 0.999

  12. Cot-Death Evidence • Here M=Murder, D=Deaths, S=SIDS • P(M|D) is not obviously close to unity!! • Like DNA evidence statistical arguments are not probative unless P(S) can be assigned.

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