> That framing actually stops holding for continuous distributions.
No, it doesn't. A continuous distribution is just a way of assigning probabilities to a parameterized set of propositions where the parameters are continuous and so the set is infinite. But for any given proposition in that set the prior is a number.
> Priors stands for prior distribution
No. Bayes's theorem is:
P(H|E) = P(E|H) * P(H) / P(E)
The "prior" is P(H) which is a probability, i.e. a number between 0 and 1, as are all the other "P" values. The "*" and "/" operations in Bayes's theorems are scalar multiplication and division.
No, it doesn't. A continuous distribution is just a way of assigning probabilities to a parameterized set of propositions where the parameters are continuous and so the set is infinite. But for any given proposition in that set the prior is a number.
> Priors stands for prior distribution
No. Bayes's theorem is:
P(H|E) = P(E|H) * P(H) / P(E)
The "prior" is P(H) which is a probability, i.e. a number between 0 and 1, as are all the other "P" values. The "*" and "/" operations in Bayes's theorems are scalar multiplication and division.