Dear BUGS users,

I asked a question about mv.car, which is posted below. Many
thanks to Professor Nicky Best. She gave me prompt and very detailed
response. Part of her email is posted below for those who are
interested in this topic.

Basically, I got the conditional and joint covariance mixed up and asked
the wrong question. I was wondering that since the joint covariance
matrix is singular, what we should do with its determinant. But with fixed
adjacency matrix, this part is constant and does not appear in the full
conditionals.

I want to point out that Prof. Best confirmed that number of islands is
counted for in both univariate car.normal and multivariate mv.car.

Best regards,

-haijun

##############################
Prof. Best's response:
> The inverse covariance matrix in mv.car distribution is the inverse
> covariance of the *conditional* distribution of the vector of random
> effects *in area i* given all the other random effects. This
conditional
> distribution is well defined. It is the covariance matrix of the
*joint*
> distribution of all the random effects that is singular, but this is
not
> what you are putting the wishart prior on. The sum-to-zero constraint
> imposed by winbugs ensures identifiability of the joint distribution.
>
> The same goes for the univariate car.normal - the univariate
conditional
> distributions are well defined, and provided a proper prior is assumed
> for the precision tau then the posterior is proper.

########################################
My original question:
 In the oral cavity and lung cancer
> in West Yorkshire example given in the Manual, the spatial random
effects
> S are given a multivariate IAR (MIAR) prior. The full
> conditional distribution of omega involves its Wishart prior and the
> MIAR distribution for S. If S had proper MCAR a priori, the conditional
of
> omega should include det(V)^(-1/2), where V is the covariance
> matrix of S which is a function of omega. But for MIAR, V is singular. I
would
> like to know how mv.car actually deal with this problem.

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