Don't confuse random variables with their density functions. a beta random
variable ranges between 0 and 1, while a beta density function can take a
value that is greater than 1.
Kosuke
On Sun, 23 Feb 2003 dhopkins(a)fas.harvard.edu wrote:
Dear All,
In the first stage of a beta binomial, we select a Pi_j from a beta binomial
distribution, having set our parameters (gamma and mu, although they could be
alternately specified as alpha and beta). But what confuses me is the fact
that many beta distributions have values of P(y) that are larger than 1,
meaning they cannot be a probability. How, then, can we select a probability
from the beta distribution--should we use P(y) to weight the probability with
which we will select a value between 0 and 1?
Best,
Dan
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