Allele Frequencies

Allele Frequency estimation

-doMaf [int]

INT=1 bfgs known minor

INT=2 EM known minor

INT=4 BFGS unknown minor

INT=8 EM unknown minor

INT=16 frequencies from genotype probabilities

Multiple estimators can be used simultaniusly be summing up the above numbers. Thus -doMaf 7 (1+2+4) will use the two first estimators

Allele frequencies from genotype likelihoods

The allele frequency estimators are described in citation. For testing reasons two optimazations are availeble. The BFGS and the EM algorithm. The EM algorithm is much faster then the BFGS. The allele frequencies are estimated by assuming that the site is diallelic and the major or minor alleles can be infered prior to the estimation or the uncertaincy of the minor allele can be incorborated into the model.

ML estimator with known minor

First infer the Major and Minor allele and then use BFGS optimazation to estimate the allele frequencies. $L(D|f)\propto \prod _{i}^{N}p(D_{i}|f)=\prod _{i}^{N}\sum _{g\in \{0,1,2\}}p(D_{i}|G=g)p(G=g|f)$ ${\hat {f}}=argmax_{f}L(D|f)$

Let $\{M,m\}$ denote the two possible alleles at the diallelic site, then the maximum likelihood estimate of this pair is found using the likelihood function

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

ML estimator with unknown minor

First infer the Major and Minor allele and then use the EM algorithm to estimate the allele frequencies.

Estimator from genotype probabilities

If the genotype probabilities are known the frequencies can be estimated by summing up the posterior probabilities $p(G=g|D)$ where $D$ is the sequencing data and $g\in \{0,1,2\}$ the allele count of the minor allele. The frequency estimate

${\hat {f}}={\frac {1}{2N}}\sum _{i}^{N}\left(2p(G=2|D)+p(G=1|D)\right)$