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 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

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.

The Argument The frequency of natural cot-deaths (SIDS) in affluent non-smoking families is about 1 in 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.

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 Changes the odds significantly unless X and Y are independent

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.

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…

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

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

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

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

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.