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