But it seems quite bizarre that somebody might be convicted purely on a statistical basis, i.e. based on a favoured Bayesian prior.
And what about politically controversial statistics and priors? Is there really any particular reason why a Bayesian shouldn't have a significantly higher prior probability that members of certain ethnic or religious groups commit certain crimes (whatever the reasons for that may be), based on government statistics? And then convict them at a relatively high rate based on this (assuming convictions using Bayesian priors don't contribute to future statistics used in Bayesian priors - to prevent double-counting of evidence)? Oops!
The judge in the Sally Clark case also stated his belief (in other words) that convinction should not be based on priors alone, but that there should be compelling evidence specific to the case as well.
Here is a paper discussing the problem. I don't know if you can access that.
It doesn't seem to me to be a problem that can be resolved easily and simply. For example in a case of terrorism, we may prefer a likelihood of guilt (derived in whatever manner) to be sufficient cause to convict. And if a woman had, say, 5 children die ostensibly of "SIDS", then even if there was no specific evidence to suggest that it was murder rather than SIDS, the Bayesian likelihood of guilt would be so very high that it would seem to override concerns about convicting based on a prior.
It doesn't seem to me that criminal cases are merely a matter of convicting based on likelihood of guilt, natural as that may sound. There are other human values to consider.
But it seems quite bizarre that somebody might be convicted...on a favoured Bayesian prior.
How would you describe how an ideal jury should perform its task? Not how real ones work, but an ideal one.
Is there really any particular reason why a Bayesian shouldn't have a significantly higher prior probability that members of certain ethnic or religious groups commit certain crimes (whatever the reasons for that may be), based on government statistics?
Conviction should not be based merely on probability of guilt; consider for example where society has
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.