User:Hussein Alasadi/Notebook/stephens/2013/10/03
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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>  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>  
  And equivalently we could derive the distribution <math> X_1  X_2, M </math>  +  And equivalently we could derive the distribution <math> X_1  X_2, M </math> <math> (f_{i,k,1}  f_{i,k,2}, .... , f_{i,k,p}, M) </math> 
*'''Likelihood for frequency a the test SNP t given all data'''  *'''Likelihood for frequency a the test SNP t given all data''' 
Revision as of 00:02, 17 October 2013
analyzing pooled sequenced data with selection  Main project page Next entry 
Notes from MeetingConsider a single lineage for now. X_{j} = 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 X_{j}
f_{i,k,j} = 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 j = 1
We assume a prior on our vector of frequencies based on our panel of SNPs (M) of dimension 2mxp ~ MVN(μ,Σ)
where if i = j or if i not equal to j
(f_{i,k,2},....,f_{i,k,p})  f_{i,k,1},M ~ The conditional distribution is easily obtained when we use a result derived here. let X_{2} = (f_{i,k,2},....,f_{i,k,p}) and X_{1} = f_{i,k,1} X_{2}  X_{1},M ~ Thus And equivalently we could derive the distribution X_{1}  X_{2},M (f_{i,k,1}  f_{i,k,2},....,f_{i,k,p},M)
let
Confused here, can we just use the expression derived above for . Also, isn't ~ N(μ_{1},Σ_{11}) and f^{obs}  M ~ N(μ_{2},Σ_{22}). But, how do we then incorporate β into the likelihood calculation?
Then: ~ N(μ,σ^{2}Σ) The parameter σ^{2} allows for overdispersion f^{obs}  M ~ N_{p − 1}(μ_{2},σ^{2}Σ_{22} + ε^{2}I) where ε^{2} allows for measurement error. and I don't understand . Shouldn't it come from (2.12) and not (2.13)  ask Matthew
