the following likelihood model for the data: (1) where μk is the parameter of a Binomial distribution for genotype k. μk models the expectation that for a given genotype k, a randomly sampled allele will be the reference allele. Intuitively, we should expect μaa to be close to 1, μab to be close to 0.5 and μbb to be close to 0. Thus, the key intuition is that for genotype k=aa, the Binomial distribution defined by μaa should be highly skewed toward the reference allele. Similarly, μbb would be skewed toward the non−reference allele. For μab, the distribution would be much more uniform. We impose a prior on the genotypes, Gi|π∼ Multinomial(Gi|π, 1) where π(k) is the prior probability of genotype k. Given knowledge of all the parameters, θ=(μ1:3, π), we can use Bayes' rule to infer the posterior over genotypes, γi(k)=p(G=k|ai, Ni, θ), where: (2) Table 1.Description of random variables in SNVMix1 and SNVMix2ParameterDescriptionValueδDirichlet prior on π(1000,100,100)πMultinomial distribution over genotypesEstimated by EM (M-step)GiGenotype at position iEstimated by EM (E-step)aijIndicates whether read j at position i matches the referenceObserved in SNVMix1, latent in SNVMix2zijIndicates whether read j aligns to its stated positionLatentqijProbability that base call is correctObserved (SNVMix2 only)rijProbability that
