Re: WinBugs Conditional Formulation
- From: "Anon." <bob.ohara@xxxxxxxxxxx>
- Date: Tue, 20 Mar 2007 20:26:41 +0200
Jean wrote:
On Mar 16, 1:51 pm, "Anon." <bob.oh...@xxxxxxxxxxx> wrote:No I'm not, and it's not too clear to me what the full model is (I don't work with these sorts of problems!). However, some thoughts, in the hope that they're useful:Jeanwrote:Thanks Prof O'Hara. After thinking about this a bit more, I think whatI realize that this should be probably be an easy question, but I'mNo, they're stochastic nodes: draw the DAG and it should become clear.
drawing a mental block. Any suggestions on the following problem
would be appreciated.
Problem: I have a large simulation program that, given a set of fixed
input conditions, provides a random response D.
The general problem is structured: P(D|a,g,h) P(g) P(h) P(a | b) P(b|
c) P( c) . G, H, C are random variables with random statistical
charateristics, e.g. mean and variance are random variables. Once C is
sampled, I know P(b|c) and P(a|b) [fixed probabilities]. One goal of
the analysis is to characterize the CDF of P(D| c) .
It seems to me that this should be relatively easy to setup in
Winbugs, but I seem to be making it more complicated than it should
be. Can I treat the parameters P(a | b) and P(b|c) as just weights?
Any suggestions on a WinBugs formulation would be very welcome.
Of course, your proability densities have to be ones that BUGS supports
(unless you want to start playing with the ones trick).
It's difficult to give more precise advice, without knowing the details
of the model.
Bob
--
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB:www.jnr-eeb.org
I have is a situation involving stratified sampling, probably with
clusters of two different variables. The probabilities are actually
the probability of a sample being from one of the clusters for
variable 1 and again for variable 2. The 5 clusters for variable 1 are
broken down into 10 clusters for variable 2 and a random sample is
taken from each of the 50 resulting cells. Are you aware of any simple
examples of stratified sampling with MCMC? I've gone through the
examples that come with Winbugs.
You have a 5x10 grid, and each individual can be in one cell. So if p_ij is the probability that an individual is in cell ij, you can model the group membership (for a single individual) as such:
model {
for(i in 1:5) {
# which category in group 1 the individual belongs to
var1[i] ~ dcat(p1[])
for(j in 1:10) {
# which category in group 2 the individual belongs to
# Probability depends on var1
var2[i,j] ~ dcat(p2[j,])
}
}
# Priors: could also set alpha in the data.
p1[1:5] ~ ddirch(alpha[1:5])
for(i in 1:5) {
p2[i, 1:10] ~ ddirch(alpha[])
}
for(i in 1:10) { alpha[i] <- 1 }
}
Of course, if you know p1 and p2, you can set them directly.
I hope this helps!
Bob
P.S. I'm not a professor, although any reasonable offers accepted...
--
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: www.jnr-eeb.org
.
- References:
- WinBugs Conditional Formulation
- From: Jean
- Re: WinBugs Conditional Formulation
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- Re: WinBugs Conditional Formulation
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