My Math Forum Projection of a distribution according to another one,

 April 23rd, 2012, 09:08 PM #1 Newbie   Joined: Sep 2009 Posts: 28 Thanks: 0 Projection of a distribution according to another one, Hi, I have the following question: Let $p, q$ defined as probability distributions over a finite sample space $\Omega=1,2,3...n$ The elements of $p$ (resp. $q$) are $p_i=p(i)$ (resp. $q_i=q(i)$)$\ \ \forall i \in [1,n]$ and we have $p \sim \mathcal{N}(\mu, \sigma),\ q \sim \mathcal{Pois}(\lambda)$ I want to find a distribution $\ q' \sim \mathcal{Pois}(\lambda'\$" /> defined as a projection (or a reduction) of the distribution $p$ with respect to the third distribution $q$. In other words, $q'$ is built by sampling $p$ according to the knowledge of the distribution $q$. If $q$ is a poisson then $q'$ will contain the $p_k$ that fit the most a poisson distribution ($q$). How can I solve this ? do I need to use bayesian inference (posterior, prior, likelihood...) ? supervised learning ? Thanks a lot !

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