Dear WinBugs users,
I am trying to use Wishart distribution to define an informative prior on
the covariance matrix for multivariate normal distribution (MVN). I define
the R (scale matrix in Wishart) as (k-p-1)*Var, where k is the df in
Wishart, p is the rank of R, Var is my prior information about the
expectation of the covariance matrix for MVN. This formula is from Classic
BUGS manual (version 0.5) section 9.10.3. I am wondering if this is a
correct way to do that and how big I should set k.
I have a little confusion about the use of Wishart in the examples
attached with WinBugs1.4.
In the example, Birats: a bivariate normal hierarchical model, a vague
Wishart prior was used by setting k=p, but set R as
R = | 200, 0 |
| 0, 0.2 |
to represents the prior guess at the order of magnitude of the covariance
matrix in MVN. What is the purpose to set R as this? Does R have any
effect on the posterior covariance matrix in MVN when the prior is
non-informative? As stated in another example, Jaws: repeated measures
analysis of variance, "except for cases with very few individuals, the
choice of R has little
effect on the posterior estimate of covariance matrix (Lindley, 1970)".
Thanks in advance,
Jianbin
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