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All you've shown here is that if you optimize one loss function (average number of people dying), you may do badly on another loss function (maximum number of p
by jules 12y ago
All you've shown here is that if you optimize one loss function (average number of people dying), you may do badly on another loss function (maximum number of people dying). Or if you are completely wrong about your prior, then you may do badly too. It's a classic "garbage in, garbage out" situation. This reminds me of the Charles Babbage quote:
"On two occasions I have been asked, 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."
Furthermore, the frequentist method doesn't do well either, they just aren't eating most of the berries (and the berries that they are eating, are the wrong ones!). If apparently eating berries isn't worth much to you, but dying has a big negative cost, you should give that to the Bayesian loss function, and it too will be conservative about eating berries. I'm very surprised that you seriously consider a method that lets you eat the more poisonous berries, simply because they are rarer, a valid criticism of Bayesianism! If you had given the correct loss function to the Bayesian, he would simply only let 20% of the people eat berries, but that 20% would be eating the mostly edible berries, and not the mostly poisonous berries of course.
Saying that Bayesians also care about things that did not happen because one of edible/inedible is something that did not happen is a bad comparison. It is unknown whether the berry is edible/inedible, so it makes sense that we consider both. On the other hand, it is known that the berry is blue, so why would we care about what if it was red?