On the second point—fair enough, though even under Bayes it’s sometimes reasonable to want a single answer on account of you only get to actually do one thing.
If you have that prior and you maximize P(model|data) on solutions with a zero probability mass on either P(data|model) or P(model), you’re screwing up multiplication.
Well, the point is that if you have a continuous-space, then the maximum-likelihood solution will have zero entries with positive probability, but the posterior probability of a zero entry is 0.
How? If any of the probabilities that the posterior probability factors into are zero, the product is also zero. Or do you just mean that since data are unlimited precision in a continuous space, no answer can ever have a positive probability because it’s infinitely unlikely?
On the second point—fair enough, though even under Bayes it’s sometimes reasonable to want a single answer on account of you only get to actually do one thing.
If you have that prior and you maximize P(model|data) on solutions with a zero probability mass on either P(data|model) or P(model), you’re screwing up multiplication.
Well, the point is that if you have a continuous-space, then the maximum-likelihood solution will have zero entries with positive probability, but the posterior probability of a zero entry is 0.
How? If any of the probabilities that the posterior probability factors into are zero, the product is also zero. Or do you just mean that since data are unlimited precision in a continuous space, no answer can ever have a positive probability because it’s infinitely unlikely?