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January 20

Integral

Suppose you have some general prior distribution $p$ . Can you show that $\int p({\vec {\alpha }})\prod _{k=1}^{N}\alpha _{k}^{n_{k}}d{\vec {\alpha }}=O\left(\prod _{k=1}^{N}\left({\frac {n_{k}}{\sum _{j=1}^{N}n_{j}}}\right)^{n_{k}}\left(\sum _{j=1}^{N}n_{j}\right)^{\frac {1-N}{2}}\right)$ ? The integral is taken over all vectors whose entries are in $[0,1]$ and sum to 1. --AnalysisAlgebra (talk) 06:00, 20 January 2013 (UTC)[reply]