SYKmaf

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

$P(D|M,f)=\prod _{i}P(D_{i}|M,f)=\sum _{m}\sum _{A_{1},A_{2}}P(D_{i}|G=A_{1}A_{2})p(G=A_{1}A_{2}|m,M)p(m),$