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

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(Notes from Meeting)
(Notes from Meeting)
Line 64: Line 64:
 
let <math>f_{obs} = \prod_{j \not= t} f_{i,k,j} </math>
 
let <math>f_{obs} = \prod_{j \not= t} f_{i,k,j} </math>
  
<math> L(f_{i,k,t}^{true}) = P(f_{obs} | f_{i,k,t}^{true}, M) = \frac{P( f_{i,k,t}^{true}  | M, f_{obs}) P(f^{obs}|M)}{P(f_{i,k,t}^{true} | M}</math>
+
<math> L(f_{i,k,t}^{true}) = P(f_{obs} | f_{i,k,t}^{true}, M) = \frac{P( f_{i,k,t}^{true}  | M, f_{obs}) P(f^{obs}|M)}{P(f_{i,k,t}^{true}) | M}</math>
  
 
where
 
where
 +
  
  

Revision as of 18:21, 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

  • Likelihood for frequency a the test SNP t given all data

let

where