I am reminded of this paper written by philosopher Neven Sesardic regarding the Sally Clark case: www.ln.edu.hk/philoso/staff/sesardic/getfile.php?file=SIDS.pdf
I quote from the Guardian article:
When Sally Clark was convicted in 1999 of smothering her two children, jurors and judges bought into the claim that the odds of siblings dying by cot death was too unlikely for her to be innocent. In fact, it was statistically more rare for a mother to kill both her children. Clark was finally freed in 2003.
In the original trial, the prosecution used probabilistic reasoning as a minor element of their case. This prompted several prominent statisticians to intervene, criticising the prosecution’s statistical methods using Bayes’s Theorem. I have also seen comments on lesswrong referring to this intervention as a positive example of Bayesian reasoning.
The kicker is, Sesardic conducts his own analysis using Bayes’s Theorem and finds that the professional statisticians’ analyses were seriously flawed and in fact according to his calculations, Clark was probably guilty after all. I find the paper very convincing and I expect that most here would find it worth reading.
Clearly, the use of Bayes’s Theorem by trained statisticians is insufficient guarantee of rational verdicts. After all it takes a small statistical error to render the posterior probability estimate wildly inaccurate (Sesardic estimates probability of guilt >0.9, whereas one statistician estimated 0.04). Clearly Bayes’s Theorem is not immune to the GIGO principle, and its use may in fact decrease the quality of an individual’s judgements since his handling of statistics may lack the garbage rejection properties of his brain’s native pattern-recognition faculties. In light of this I think it is perfectly reasonable to question whether a general increase in the use of statistical methods in court would be likely to improve the accuracy of verdicts.
Having said that, if an individual is perspicacious (as for example Neven Sesardic and Eliezer Yudkowsky are) then the use of Bayes’s Theorem to evaluate criminal cases is likely to improve accuracy. The problem is that most people are not perspicacious, nor is a lecture on the use of Bayes’s Theorem likely to make them so (as the Sally Clark example demonstrates quite clearly).
I am reminded of this paper written by philosopher Neven Sesardic regarding the Sally Clark case: www.ln.edu.hk/philoso/staff/sesardic/getfile.php?file=SIDS.pdf
I quote from the Guardian article:
In the original trial, the prosecution used probabilistic reasoning as a minor element of their case. This prompted several prominent statisticians to intervene, criticising the prosecution’s statistical methods using Bayes’s Theorem. I have also seen comments on lesswrong referring to this intervention as a positive example of Bayesian reasoning.
The kicker is, Sesardic conducts his own analysis using Bayes’s Theorem and finds that the professional statisticians’ analyses were seriously flawed and in fact according to his calculations, Clark was probably guilty after all. I find the paper very convincing and I expect that most here would find it worth reading.
Clearly, the use of Bayes’s Theorem by trained statisticians is insufficient guarantee of rational verdicts. After all it takes a small statistical error to render the posterior probability estimate wildly inaccurate (Sesardic estimates probability of guilt >0.9, whereas one statistician estimated 0.04). Clearly Bayes’s Theorem is not immune to the GIGO principle, and its use may in fact decrease the quality of an individual’s judgements since his handling of statistics may lack the garbage rejection properties of his brain’s native pattern-recognition faculties. In light of this I think it is perfectly reasonable to question whether a general increase in the use of statistical methods in court would be likely to improve the accuracy of verdicts.
Having said that, if an individual is perspicacious (as for example Neven Sesardic and Eliezer Yudkowsky are) then the use of Bayes’s Theorem to evaluate criminal cases is likely to improve accuracy. The problem is that most people are not perspicacious, nor is a lecture on the use of Bayes’s Theorem likely to make them so (as the Sally Clark example demonstrates quite clearly).
Clickable link: http://www.ln.edu.hk/philoso/staff/sesardic/getfile.php?file=SIDS.pdf