BIC is a sub model selection procedure For an observation y R n y R n , BIC adds the penalty 1 2 d log n 1 2 d log n to the maximized log log likelihood for sub models of dimension d d Deduce from the preceding example that this version of BIC cannot be a Bayes procedure ...

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BIC is a sub-model selection procedure. For an observation y R n y R n

Question:

BIC is a sub-model selection procedure. For an observation $y \in R^{n}$ , BIC adds the penalty $- \frac{1}{2} d \log n$ to the maximized $\log$ likelihood for sub-models of dimension $d$ . Deduce from the preceding example that this version of BIC cannot be a Bayes procedure.