ANGSD: Analysis of next generation Sequencing Data

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SYKmaf

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Revision as of 18:49, 15 December 2014 by Albrecht (talk | contribs) (ML estimator with unknown minor)

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ML estimator with known minor

First infer the Major and Minor allele and then use BFGS (-doMaf 1) optimazation or the EM algorithm (-doMaf 2) to estimate the allele frequencies.


L(D|f) \propto \prod_i^N p(D_i|f) = \prod_i^N \sum_{g\in\{0,1,2\}}p(D_i|G=g)p(G=g|f)


  \hat{f}=argmax_{f} L(D|f)

ML estimator with unknown minor

First infer the Major allele and then use BFGS (-doMaf 4) optimazation or the EM algorithm (-doMaf 8) to estimate the allele frequencies. Here only the Major allele needs to be known and the uncertaincy of infering the minor allele is modelled.

Let \{M,m\} denote the major an minor allele assuming adiallelic site, then the maximum likelihood estimate of this pair is found using the likelihood function


  P(D|M,f) =   \prod_i P(D_i|M,f) =  \prod_i \sum_m \sum_{A_1,A_2} P(D_i|G=A_1A_2)p(G=A_1A_2|m,M)p(m),