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.)
