Hello Group,
I have a problem that I hope somebody has solved before. I have a two
random variables that follow a bivariate normal distribution with mean vector mu
(a 1 x 2 vector) and covariance matrix sigma (a 2 x 2 matrix). I have to
constrain the variance of the first variable to be equal to 1 in this particular
application. This seems easy enough at first glance, but WinBUGS does not model
the variance-covariance matrix, sigma, but instead models the precision matrix,
tau, where tau=inverse(sigma). Consequently, this one constraint on the first
element of sigma, has implications on all of the elements of its inverse. In
essence, I would like to use the following distributions with WinBUGS:
theta[i,1:2] ~ dmnorm(mu[],tau[,]);
tau[1:2,1:2] ~ dwish (R[ , ],2);
but with the constraint that tau=inverse(sigma) and sigma[1,1]=1. My student
and I have tried many things that WinBUGS would not allow for one reason or
another. Has anybody had a similar problem that they have solved? Thanks in
advance for your assistance.
Best Wishes,
Jim Roberts
********************************
James S. Roberts, Ph.D.
Associate Professor
Georgia Institute of Technology
School of Psychology
654 Cherry Street
Atlanta, GA 30332-0170
Phone: (404) 894-6069
Fax: (404) 894-8905
********************************
-------------------------------------------------------------------
This list is for discussion of modelling issues and the BUGS software.
For help with crashes and error messages, first mail [log in to unmask]
To mail the BUGS list, mail to [log in to unmask]
Before mailing, please check the archive at www.jiscmail.ac.uk/lists/bugs.html
Please do not mail attachments to the list.
To leave the BUGS list, send LEAVE BUGS to [log in to unmask]
If this fails, mail [log in to unmask], NOT the whole list
|