The Inexpert Witness <ul><li>Sir Roy Meadow, born 1933 </li></ul><ul><li>Distinguished paediatrician </li></ul><ul><li>Fam...
The Case of Sally Clark <ul><li>Solicitor Sally Clark was tried in 1999 for the murder of two children (Christopher, 11 we...
Publish and be damned <ul><li>This case was mentioned in my book “From Cosmos to Chaos” </li></ul><ul><li>In 2005, Meadow ...
The Argument <ul><li>The frequency of natural cot-deaths (SIDS) in affluent non-smoking families is about 1 in 8500. </li>...
Independence <ul><li>There is strong evidence that the SIDS does have genetic or environmental factors that may correlate ...
The Prosecutor’s Fallacy <ul><li>Even if the probability calculation were right, it is the wrong probability.  </li></ul><...
Inverse Reasoning <ul><li>If we calculate P(Deaths|SIDS) to be very small, that does not necessarily mean that P(Murder|De...
A Load of Balls… <ul><li>Two urns A and B. </li></ul><ul><li>A has 999 white balls and 1 black one; B has 1 white balls an...
Urn A Urn B 999 white 1 black 999 black 1 white P(white ball | urn is A)=0.999, etc
Bayes’ Theorem: Inverse reasoning <ul><li>Rev. Thomas Bayes (1702-1761) </li></ul><ul><li>Never published any papers durin...
Bayes’ Theorem <ul><li>In the toy example, X is “the urn is A” and Y is “the ball is white”. </li></ul><ul><li>Everything ...
Cot-Death Evidence <ul><li>Here M=Murder, D=Deaths, S=SIDS </li></ul><ul><li>P(M|D) is not obviously close to unity!! </li...
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The Curious Case of the Inexpert Witness

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A short tutorial to Bayesian probability, in the light of the case of Sally Clark and the misleading use of statistical reasoning by Sir Roy Meadow at her trial.

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The Curious Case of the Inexpert Witness

  1. 1. The Inexpert Witness <ul><li>Sir Roy Meadow, born 1933 </li></ul><ul><li>Distinguished paediatrician </li></ul><ul><li>Famous for “Munchausen Syndrome by Proxy” </li></ul><ul><li>Expert witness in cases of suspected child abuse and murder </li></ul><ul><li>Notorious for high-profile miscarriage of justice in Sally Clark trial </li></ul>
  2. 2. The Case of Sally Clark <ul><li>Solicitor Sally Clark was tried in 1999 for the murder of two children (Christopher, 11 weeks), (Harry, 8 weeks). </li></ul><ul><li>Medical testimony divided </li></ul><ul><li>Meadow’s evidence was decisive, but flawed. </li></ul><ul><li>Appeal in autumn 2000 was dismissed </li></ul><ul><li>Second appeal (for different reasons) in 2003, but ruling cast doubt also on Meadow’s testimony; Clark released. </li></ul><ul><li>Sally Clark died on16 March 2007 of alcohol poisoning </li></ul>
  3. 3. Publish and be damned <ul><li>This case was mentioned in my book “From Cosmos to Chaos” </li></ul><ul><li>In 2005, Meadow appeared before a GMC tribunal and was struck off </li></ul><ul><li>He appealed and pending the outcome my book was shelved by OUP </li></ul><ul><li>His appeal succeeded, but was guilty of “serious professional misconduct” so it was published. </li></ul>
  4. 4. The Argument <ul><li>The frequency of natural cot-deaths (SIDS) in affluent non-smoking families is about 1 in 8500. </li></ul><ul><li>Meadow argued that the probability of two such deaths in one family is this squared, or about 1 in 73,000,000. </li></ul><ul><li>This was widely interpreted as meaning that these were the odds against Clark being innocent of murder. </li></ul><ul><li>The Royal Statistical Society in 2001 issued a press release that summed up the two major flaws in Meadow’s argument. </li></ul>
  5. 5. Independence <ul><li>There is strong evidence that the SIDS does have genetic or environmental factors that may correlate within a family </li></ul><ul><li>P(second death|first)=1/77, not 1 in 8500. </li></ul><ul><li>Changes the odds significantly </li></ul>unless X and Y are independent
  6. 6. The Prosecutor’s Fallacy <ul><li>Even if the probability calculation were right, it is the wrong probability. </li></ul><ul><li>P(Murder|Evidence) is not the same as P(Evidence|Murder), although ordinary language can confuse the two. </li></ul><ul><li>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? </li></ul><ul><li>No! </li></ul><ul><li>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. </li></ul>
  7. 7. Inverse Reasoning <ul><li>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! </li></ul><ul><li>We need to invert the reasoning to produce P(SIDS|Deaths) and P(Murder|Deaths) both of which are small! </li></ul><ul><li>The only fully consistent way to do this is by Bayes’ Theorem, although a (frequentist) likelihood ratio would also do… </li></ul>
  8. 8. A Load of Balls… <ul><li>Two urns A and B. </li></ul><ul><li>A has 999 white balls and 1 black one; B has 1 white balls and 999 black ones. </li></ul><ul><li>P(white| urn A) = .999, etc. </li></ul><ul><li>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? </li></ul><ul><li>P(Urn A| white) requires “inverse” reasoning: Bayes’ Theorem </li></ul>
  9. 9. Urn A Urn B 999 white 1 black 999 black 1 white P(white ball | urn is A)=0.999, etc
  10. 10. Bayes’ Theorem: Inverse reasoning <ul><li>Rev. Thomas Bayes (1702-1761) </li></ul><ul><li>Never published any papers during his lifetime </li></ul><ul><li>The general form of Bayes’ theorem was actually given later (by Laplace). </li></ul>
  11. 11. Bayes’ Theorem <ul><li>In the toy example, X is “the urn is A” and Y is “the ball is white”. </li></ul><ul><li>Everything is calculable, and the required posterior probability is 0.999 </li></ul>
  12. 12. Cot-Death Evidence <ul><li>Here M=Murder, D=Deaths, S=SIDS </li></ul><ul><li>P(M|D) is not obviously close to unity!! </li></ul><ul><li>Like DNA evidence statistical arguments are not probative unless P(S) can be assigned. </li></ul>

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