VanderPlas (UW) and I continued working on the cross-validation and Bayes integral comparison. I am optimistic because both quantities have exactly the same units (or dimensions). I am pessimistic because the Bayes integral involves the prior and the cross-validation doesn't. VanderPlas has some conditions under which he thinks they could be the same, but neither of us is convinced that those conditions could really be met in practice. I am wondering if they could be met in a very successful hierarchical analysis. Anyway, this is all very vague because we don't have a clear example. By the end of the day we nearly had a document and we had a plan for an example problem where we can work everything out explicitly and (more or less) exactly.
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