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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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