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Abstract:
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Objective Bayes criteria for model selection crucially depend on n, the "sample size." It appears explicitly in the formulae of asymptotic Bayes factors (Laplace, BIC and generalizations, etc.). Similarly, it is often used when choosing of the appropriate scale for objective (but proper) priors, which are generally needed to compute Bayes factors or posterior odds, or, more generally, in Bayes analysis under model uncertainty. There are, however, some difficulties in defining "n," some of which are explored in this talk. Although there have been some attempts towards appropriately defining "n," the problem remains essentially open. We provide in this talk a new definition which seems to apply satisfactorily to challenging situations, including examples for which the previous definitions fail. We call it TESS (The Effective Sample Size).
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