Re-reading that Sesardic paper set me to thinking about further issues relating to use of statistical evidence in criminal cases. In this post Yudkowsky points out that whilst all legal evidence should ideally be rational evidence, not all rational evidence is suitable as legal evidence. This is because certain rational evidence sources would become systematically corrupted and cease to function as such, if they were liable to be used as legal evidence (he uses as an example the police commissioner's confidential disclosure to a friend of the identity of the city's crime boss).
In Sesardic's paper, he calculates (using the same statistical sources chosen by the statisticians that he is criticising) that the prior probability of a mother such as Sally Clark, who has had two infants die in succession for no apparent medical reason, being guilty of double murder is 25 times greater than the prior probability of her children having both died innocently through "SIDS" (ignoring the probability of one infant having died of SIDS and the other having been murdered, which is very tiny and superfluous to the analysis). This is before he gets to the Bayesian effect of the evidence from the specific case, which turns out to increase the likelihood of the double murder hypothesis at the expense of the double SIDS hypothesis.
Clearly (if Sesardic is convincing) Sally Clark should have been found guilty. But what if the evidence from the alleged crime scenes had been indecisive, i.e. the likelihood ratio were ~1? In this case, Bayes’s Theorem tells us that Clark is very probably guilty, but this is essentially a judgement based on statistics alone. Would it be proper for courts to convict based on this kind of result from an application of Bayes’s Theorem, assuming that said analysis had been subjected to rigorous scrutiny and appeared highly convincing to the jury? My gut feeling is no - that this is of a similar class to Yudkowsky’s rational, but not suitable legal evidence. But I’d have to think some more before defending that statement.
Would it be proper for courts to convict based on this kind of result from an application of Bayes’s Theorem, assuming that said analysis had been subjected to rigorous scrutiny and appeared highly convincing to the jury?
It would be no different than other cases of conviction or lack thereof under similar odds. Whether people who probably guilty but have an X% chance of being innocent go free or not should not depend on how jurors concluded X.
This is an interesting article talking about the use of bayes in british courts and efforts to improve how statistics are used in court cases. Probably worth keeping an eye on. It might expose more people to bayes if it becomes common and thus portrayed in TV dramas.