second and higher-order probabilities

lolgarithms

Why do I never hear of "second-order probabilities" (probability that the probability of an event is x. for example, you pick a box at random out of 3 boxes, and each box can have either 1, 3 or 5 red marbles out of six marbles)? can measurement or calculation of probability not be affected by random and inaccurate data?

EnumaElish

How is your concept different from joint probability? How is it different from conditional probability?

Alternatively, you can define higher-order probability as follows. Let P = Prob{X < x} = CDF(x). Since X is a random variable, so is P (because it is a function of a random variable, with CDF of X as the link function). As a random variable, P is distributed uniformly over [0,1]. Defined this way, higher-order probabilities are not interesting: they are all distributed uniformly over [0,1].

mXSCNT

Decision theory does sometimes use second-order probabilities, although they are distrusted by some.

google has the answers.