## LESSWRONGLW

No. This was already discussed here.

If she had been randomly sampled from the general population then the prior probability would have been exceedingly small, but she wasn't randomly sampled, she was investigated because she lived with the victim. When someone is murdered, there is a high probability that the perpetrator is somebody in a close or frequent relationship with them.

Realistically, the prior probability of Knox being a perpetrator would be around 0.01, the same for Sollecito, with high positive correlation between them.

I disagree strongly. The fact that she lives with the victim doesn't shield off the effect of her demographic profile on the likelihood she committed the crime.

Let's analyze the problem using Bayes Net terminology. Let A={suspect=Knox's demographic profile}, B={suspect lives with victim} and C={suspect guilty}. Then your claim is that the net is structured as A->B->C, or that the demographic evidence is conditionally independent of guilt given co-habitation. My claim is that the net is structured as A->C<-B; both A and B affect the likelihood ... (read more)

8gwern5yThat's still base-rate neglect as you are picking and choosing what you want to look at and not conditioning on one of the more relevant variables. What fraction of the pretty girls who lived with the victims turned out to be murderers? By looking at the genderless conditional probability ('somebody'), you're implying that women like Knox might have male-like murder levels, which is obviously wrong. And to the extent that pretty girls do not have differing patterns of murdering roommates from other women, you're making the exact same mistake, even (it doesn't matter whether you update on pretty girl then roommate or roommate then pretty girl). Update on both living with the victim and being female and the small probability is bigger but... still small, since the still relatively low probability of a roommate murdering is penalized substantially by being female (female murder rates are like 1/10th male and that's the raw rates, not adjusted for age or SES or race etc). As the top comment says, "Once we take into account that AK and MK aren't in a relationship, AK is female, and there is very strong evidence that someone else committed the murder then I'd agree that the probability drops".