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

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