The original version of the LITTERS example exhibits extremely poor
mixing.  This version uses a different parameterization in terms of
the mean mu and a parameter theta that is, approximately, the shrinkage
(It is only equal to the shrinkage when the litter sizes are all equal).

A uniform prior is given to both theta and mu. The uniform shrinkage
prior has been suggested as a reference prior in GLMMs by Natarajan,
J and Kass, RE. Reference Bayesian methods for generalized linear mixed
models, JASA, vol 95, 227-237 (2000).

The approximate uniform shrinkage prior is quite revealing in this
example.  The posterior of theta[2] is not very different from its
prior, indicating that there is very little information in the data
about this parameter.