I gave my MPIA Hauskolloquium on model selection today. I strongly advocated leave-one-out cross-validation. It is very easy, conceptually simple, robust to many kinds of mistakes (about model space and noise amplitude), and employs a "prediction" utility that matches the goals of most scientists. Despite the frequentism of all this, I am still thought-of as a Bayesian around here. I am only a Bayesian when I have to be! That turns out to be frequently.
The marginalized likelihood (marginalized over orbital phase) mentioned yesterday did work well, so Jagannath and I are ready to write our paper. We discussed the introduction for the paper and the speed of the code.