That's exactly right. pi varies acorss the draws, but mu and gamma
(parameters of beta-binomial) are fixed.
Kosuke
On Sun, 23 Feb 2003, brightjo wrote:
Kosuke,
I'm confused.
This is how I thought one sampled/drew from the beta-binomial distribution:
First, I thought the wording would be "take N (i.i.d.) draws from the
beta-binomial distribution with parameters mu and gamma". To do this, I
thought you "take" N Bernoulli draws with pi changing with each draw. Pi
changes by sampling from the beta distribution. So, for each Bernoulli trial
(with varying pi), you get either a 0 or 1 as the outcome. Therefore, to get
the result of taking N draws from the beta-binomial distribution, you add up
your N 0's or 1's from each Bernoulli trial. Thus, the result of N
beta-binomial draws will be somewhere between 0 and N.
This is what I thought, but I have found that not to be the only
interpretation of how the beta-binomial distribution works.
Can you help clear up this confusion.
Thanks,
John.
===== Original Message From Kosuke Imai
<kimai(a)fas.harvard.edu> =====
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
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l