I think you might have to "cheat", with something like this:
sd.rel <- sd(rel.star[,1])
for(i in i:N) {
rel.star[i,] ~ dmnorm(0, prec[,])
rel.star[]
for(k in 1:2) {
rel[i,k] <- mu[k] + (rel.star[i,k] - mean(rel.star[,k]))/sd.rel
}
}
(BUGS may run more quickly if you swap the i and k indices, i.e. have
rel[k,i] not rel[i,k])
I haven't checked the code, but I hope you get the idea. You might have
to be a bit careful with the priors, as the prior for rel.star[,1] will
affect the prior for rel[,2].
Bob
On 10/20/2017 10:57 PM, Ashley Lee wrote:
> Hello. All,
>
> I'm struggling with how to write a multivariate normal distribution. The mean of the multivariate normal distribution is fixed as 0 for both variables. But, the variance of one variable should be fixed to 1, while other should be free to estimate (for the model identification purpose). If both variables are free to estimate, I can simply use wishart prior to estimate variance-covariance matrix of the multivariate normal distribution. But, I MUST fix one of the variances.
>
> What I thought as a possible solution was
>
> rel ~ dmnorm(mu[], prec[,])
>
> mu[1]<-0
> mu[2]<-0
>
> prec[,] ~ dwish(s.prec[,],2)
>
> s.prec[1,1]<-1
> s.prec[2,2]<-1
> s.prec[1,2] <-0
> s.prec[2,1] <-0
>
> prec[1,1] <-1 # to fix the variance after variance-covarince matrix was sampled from the wishart distribution.
>
> But, because Openbugs does not care of which argument comes first, this did not work.
>
> Please share your idea to solve this problem with me if any.
>
> Thanks much all!
>
> Ashley
>
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--
Bob O'Hara
Institutt for matematiske fag
NTNU
7491 Trondheim
Norway
Mobile: +49 1515 888 5440
Journal of Negative Results - EEB: www.jnr-eeb.org
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