Difference between revisions of "User:Hussein Alasadi/Notebook/stephens/2013/10/03"
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< User:Hussein Alasadi  Notebook  stephens  2013  10
(→Notes from Meeting) 
(→Notes from Meeting) 

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* '''conditional distribution'''  * '''conditional distribution'''  
−  <math> (f_{i,k,2}, .... , f_{i,k,p})  f_{i,k,1}, M </math> ~ <math> MVN(\bar{\mu}, \bar{\  +  <math> (f_{i,k,2}, .... , f_{i,k,p})  f_{i,k,1}, M </math> ~ <math> MVN(\bar{\mu}, \bar{\Sigma}) </math> 
The conditional distribution is easily obtained when we use a result derived [http://openwetware.org/wiki/User:Hussein_Alasadi/Notebook/stephens/2013/10/14 here].  The conditional distribution is easily obtained when we use a result derived [http://openwetware.org/wiki/User:Hussein_Alasadi/Notebook/stephens/2013/10/14 here].  
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<math> X_2  X_1, M </math> ~ <math> N(\vec{\mu_2} + \Sigma_{21} \Sigma_{11}^{1} (x_1  \mu_1), \Sigma_{22}  \Sigma_{21}\Sigma_{11}^{1}\Sigma_{12}) </math>  <math> X_2  X_1, M </math> ~ <math> N(\vec{\mu_2} + \Sigma_{21} \Sigma_{11}^{1} (x_1  \mu_1), \Sigma_{22}  \Sigma_{21}\Sigma_{11}^{1}\Sigma_{12}) </math>  
+  Thus <math> \bar{\mu} = vec{\mu_2} + \Sigma_{21} \Sigma_{11}^{1} (x_1  \mu_1), \bar{\Sigma} = \Sigma_{22}  \Sigma_{21}\Sigma_{11}^{1}\Sigma_{12} </math>  
Revision as of 17:20, 16 October 2013
analyzing pooled sequenced data with selection  <html><img src="/images/9/94/Report.png" border="0" /></html> Main project page Next entry<html><img src="/images/5/5c/Resultset_next.png" border="0" /></html> 
Notes from MeetingConsider a single lineage for now. = frequency of "1" allele at SNP j in the pool (i.e. the true frequency of the 1 allele in the pool)
= number of "0", "1" alleles at SNP j ()
~ Normal approximation to binomial The variance of this distribution results from error due to binomial sampling. To simplify, we just plug in for
frequency of reference allele in group i, replicate and SNP j. vector of frequencies Without loss of generality, we assume that the putative selected site is site
We assume a prior on our vector of frequencies based on our panel of SNPs of dimension ~
where if i = j or if i not equal to j
~ The conditional distribution is easily obtained when we use a result derived here. let and ~ Thus
