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

= January 20 =

Integral
Suppose you have some general prior distribution $$p$$. Can you show that $$\int p(\vec{\alpha})\prod_{k=1}^N \alpha_k^{n_k}d\vec{\alpha} = O\left(\prod_{k=1}^N \left(\frac{n_k}{\sum_{j=1}^Nn_j}\right)^{n_k}\left(\sum_{j=1}^N n_j\right)^{\frac{1-N}{2}}\right)$$? 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)