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Subject:

Constraining the Inverse Variance-Covariance Matrix in a Multivariate Normal Distribution

From:

James S. Roberts

Date:

Mon, 18 Sep 2006 21:51:07 -0400

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text/plain

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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 ******************************** ------------------------------------------------------------------- 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 ```

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