Testwiki:Reference desk/Archives/Mathematics/2013 January 20

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January 20

Integral

Suppose you have some general prior distribution $p$. Can you show that $\int p(\overrightarrow{\alpha })\prod _{k=1}^N{\alpha }_k^{n_k}d\overrightarrow{\alpha }=O\left(\prod _{k=1}^N{\left(\frac{n_k}{\sum _{j=1}^N{n}_j}\right)}^{n_k}{\left(\sum _{j=1}^N{n}_j\right)}^{\frac{1-N}{2}}\right)$? 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)