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by hablog
1127 days ago
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> The proper Bayesian response... since both "being male" and any race are very weak predictors (see my other comment upthread). I saw your comment - you don't understand how bayesianism works. Look up "odds ratios" for the most salient concept that you're missing here. If P(x|!y) = 0.0000001 and P(x|y) = 0.01, this relationship is extremely powerful even though it's "weak" in the sense you're using. |
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Sure, compute the odds ratio for committing a violent crime due to being male. It is large, which in plain English means "most violent criminals are male".
But that doesn't mean the probability of a randomly chosen male being a violent criminal is large. It's still small, because you have to multiply the odds ratio by a very small prior (since the prior probability of a randomly chosen person being a violent criminal is very small). So if all you know about a person is that they are male, you still have only a very weak prediction that they might be a violent criminal. In other words, in plain English, "most males are not violent criminals".
What you need to have a strong predictor is some factor X for which not just the odds ratio but the posterior probability of being a violent criminal, conditioned on X, is large, i.e., for which you can say "most X's are violent criminals". Being male is not such a factor.