The book ** Random effects and latent variable model selection**, edited by David Dunson in 2008 as a Springer Lecture Note. contains several chapters dealing with evidence approximation in mixed effect models. (Incidentally, I would be interested in the story behind the Lecture Note as I found no explanation in the backcover or in the preface. Some chapters but not all refer to a SAMSI workshop on model uncertainty…) The final chapter written by Joyee Ghosh and David Dunson (similar to a corresponding paper in JCGS) contains in particular the interesting identity that the Bayes factor opposing model

*h*to model

*h-1*can be unbiasedly approximated by (the average of the terms)

when

- is the model index,
- the ‘s are simulated from the posterior under model
*h,* - the model only considers the
*h-1*first components of , - the prior under model
*h-1*is the projection of the prior under model*h*. (Note that this marginalisation is not the projection used in.)**Bayesian Core**