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.

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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) }

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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), }