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This is a nice insight. I slightly disagree with the first example in a gambling context, although it makes sense in the context of information theory. I don’

This is a nice insight. I slightly disagree with the first example in a gambling context, although it makes sense in the context of information theory. I don’t think the choice of prior is right when giving 20:1 posterior odds you’d be willing to bet on. A better prior should be related to the probability of a random person lying about their name when introducing themselves. And the posterior then doesn’t really depend a lot on what name he says.

layer8 3y ago
It also depends on how much hinges on the assertion being true or false. If you lose a million dollars if it turns out his name isn’t “Mark Xu”, you’d take much more care to verify the claim.
nkurz 3y ago
I'm not sure. Given that there is an individual standing in front of you, does it ever make sense to use the odds of a random individual instead of your best estimate for that particular individual? At the least, it seems likely that the circumstance in which the name is being given would change things greatly: a police officer stopping someone in the dark versus a minister introducing themselves after a sermon. In neither case does a universal estimate of lying about a name seem applicable. And the choice of name does seem important. If someone with no visible appearance of being Asian gives you a very Asian name (or vice versa), you might have a lot more doubt. And if the name is otherwise humorous (Biggus Dickus) or stereotypical (John Doe) this also should affect your estimate. Why would it be a plus that "the posterior then doesn’t really depend a lot on what name he says"?
- conformist 3y ago
  Yeah, of course, if the name is clearly absurd you’d use the insights from that and update your posterior, and if you have more information about the person you can include it in the prior. The point was that 1/n over all possible names is far from a reasonable prior, and that the Bayesian update barely depends on the name itself (within reason), but on other information gained during the introduction.

layer8 3y ago

It also depends on how much hinges on the assertion being true or false. If you lose a million dollars if it turns out his name isn’t “Mark Xu”, you’d take much more care to verify the claim.

nkurz 3y ago

I'm not sure. Given that there is an individual standing in front of you, does it ever make sense to use the odds of a random individual instead of your best estimate for that particular individual? At the least, it seems likely that the circumstance in which the name is being given would change things greatly: a police officer stopping someone in the dark versus a minister introducing themselves after a sermon. In neither case does a universal estimate of lying about a name seem applicable. And the choice of name does seem important. If someone with no visible appearance of being Asian gives you a very Asian name (or vice versa), you might have a lot more doubt. And if the name is otherwise humorous (Biggus Dickus) or stereotypical (John Doe) this also should affect your estimate. Why would it be a plus that "the posterior then doesn’t really depend a lot on what name he says"?

conformist 3y ago
Yeah, of course, if the name is clearly absurd you’d use the insights from that and update your posterior, and if you have more information about the person you can include it in the prior. The point was that 1/n over all possible names is far from a reasonable prior, and that the Bayesian update barely depends on the name itself (within reason), but on other information gained during the introduction.