Hi all,
[ My original message got rejected from the winbugs mail list so I sent
it to the ANZSTAT list. The winbugs rejection was an (e-mail server)
error and the message was subsequently posted to the winbugs list. I got
responses from both lists and I've summarised the most pertenint from
both sets of responses here. Apologies to anyone who gets double-ups. ]
.1.
A pointer to *exactly* what I wanted and in recipe format was sent to me
from Kate Cowles. It is from her lecture notes in her Bayesian stats
course. See pages 4 and 5 of the pdf.
http://www.stat.uiowa.edu/ftp/kcowles/s138/lect16.pdf
.2.
In a discussion with James O'Malley I asked what influence k has on the
Wishart distribution and at what value would it dominate the posterior.
{Severely cut and pasted - apologies if I have lost any meaning.)
...I would parameterize the prior as:
x[,] ~ dwish(R[,]/k, k) so that you get E[x] = R
k is like a divisor on the spread of the prior distribution. ... So
double the value of k and the prior variance of the
covariance will approximately halve. ... k=1000 and beyond would cause
the prior to dominate the posterior.
.3.
A noteworthy point which practically everyone reminded me of is that I
need k to be at least as large as the dimensions of R[,] or x[,] for the
distribution to be proper.
Thanks to all those who responded. I learnt heaps!
ciao,
Megan
~~~~~Original Message~~~~~
Hi,
I have a repeated measures data and I am fitting a non-linear mixed
effects model to it. The parameters in the non-linear model are going
to have a multivariate normal distribution. This is because some of my
participants don't have a full set of the repeated measures and so some
of their parameters can't be estimated well. I'd like to be able to
"borrow" information from the participants with parameters that do fit
well.
The model has been fitted before to a reasonably similar, larger data
set and I can use that as my prior information for the mean and variance
of the multivariate normal distribution. However, I don't know how to
set the degrees of freedom on the prior Wishart distribution for the
variance matrix of the mvn distribution to reflect my uncertainty. (i.e.
x[,] ~ dwish(R[,], k), I have R but don't know what to set k )
Is there a rule of thumb?
If it helps, the original data set (prior information) contains data
on 18 participants with around 100 data points per person. My data set
contains 49 people with around 21 data points per person.
Ta,
Megan
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