Bayesian Inference on Variance Components

Hi Charlie,

this paper:
Nakagawa, S. and Schielzeth, H. (2010), Repeatability for Gaussian and
non-Gaussian data: a practical guide for biologists. Biological Reviews,
85: 935?956.
http://onlinelibrary.wiley.com/doi/10.1111/j.1469-185X.2010.00141.x/abstract

with the associated website: http://rptr.r-forge.r-project.org/

may be of interest to you. They implemented (in R, using the MCMCglmm
package ) MCMC Bayesian estimation of variance components to compute
intraclass correlations with associated credible intervals (they also
have a glmmPQL + parametric bootstraping approach).

I've been playing it with myself and it may do (with a bit of tweaking
of not, depending of what you want) what you need. I'm however still
uncertain on how to choose reliable un- or weakly informative priors for
variance components in MCMCglmm. My experiments with this so far is that
it is relatively easy to get estimates that are way off the ones
provided by Laplace approximation. 

It seems that BUGS/JAGS would allow you using a wider range of prior
distribution (like half-normal), but I found them harder to use.

best, 

simon