I am really happy to see more formal Bayes on LW. Ditto for decision analysis. They get talked about frequently but I don’t usually see to much math being used.
That said I was slightly confused, specifically its pretty clear what cdf and pdf are in terms of how they are derived from probability density. However its not quite clear what you mean by probability density. Am I overlooking/misunderstanding a explanation or are we assumed to already know what it is?
A probability density is just like any other kind of density; it’s the amount of probability per unit volume. (In one-dimension, the ‘volume’ equivalent is length.) You need it when you have a continuous belief space but not when you have a discrete belief space. If you’re doing billiard ball physics with point masses, you don’t need mass densities; likewise if you’re comparing billiard ball beliefs rather than real ones (the weatherman doesn’t say “Rainy” or “Sunny” but expresses a percentage) you don’t need probability densities.
I am really happy to see more formal Bayes on LW. Ditto for decision analysis. They get talked about frequently but I don’t usually see to much math being used. That said I was slightly confused, specifically its pretty clear what cdf and pdf are in terms of how they are derived from probability density. However its not quite clear what you mean by probability density. Am I overlooking/misunderstanding a explanation or are we assumed to already know what it is?
A probability density is just like any other kind of density; it’s the amount of probability per unit volume. (In one-dimension, the ‘volume’ equivalent is length.) You need it when you have a continuous belief space but not when you have a discrete belief space. If you’re doing billiard ball physics with point masses, you don’t need mass densities; likewise if you’re comparing billiard ball beliefs rather than real ones (the weatherman doesn’t say “Rainy” or “Sunny” but expresses a percentage) you don’t need probability densities.
Ok, that makes sense.