[XorNot]

Welcome to the world of Bayesian priors, and our star witness, the OJ Simpson murder trial.

There was a comment which didn't get enough attention during that trial: the defense claimed that fewer then 1 in 1000 women who suffer domestic abuse are killed by their domestic partners and therefore allegations of spousal abuse by OJ Simpson did not constitute supporting evidence.

But: this is wrong. Because once a woman has been killed, if her domestic partner was an abuser then almost 80% of the time the abuser did it (given reasonable other factual assumptions - i.e. pretty obviously if they weren't in the same state at the time then we can exclude it etc..)

The key part of the issue is that once an event has occurred, the Bayesian prior has changed: we are no longer evaluating the same initial probability.

[1] https://math.temple.edu/~paulos/oldsite/oj.html