Difference between revisions of "User:Hussein Alasadi/Notebook/stephens/2013/10/03"

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(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{\sum}) </math>
+
<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

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Notes from Meeting

Consider 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)

  • Data:

= number of "0", "1" alleles at SNP j ()


  • Normal approximation

~ Normal approximation to binomial

The variance of this distribution results from error due to binomial sampling.

To simplify, we just plug in for

  • notation

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

  • Model

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


  • at selected site

  • conditional distribution

~ The conditional distribution is easily obtained when we use a result derived here.

let and

~

Thus