deletions | additions       diff --git a/Correcting for incorrect genotype calls.tex b/Correcting for incorrect genotype calls.tex  index 18fba5d..3fcadd5 100644  --- a/Correcting for incorrect genotype calls.tex  +++ b/Correcting for incorrect genotype calls.tex 
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+ \Pr_{\mathrm{BB}} \left(Y_{ik} = y_{ik} \left| 1-p_{\textrm{err}}, n_{ik}, \Upsilon_i \right. \right) \right] &  \end{eqnarray*}  We found that even SNPs with heterozygous probabilities of 1.0 are occasionally miscalled so we set heterozygous probabilities to a maximum value of 0.99. We then update this heterozygous probability using sequencing data obtained from the same individual. Sequencing data may consist of DNA sequence sequencing  reads or readsthat are  aggregated acrossfrom  multiple types of experiments performed on the same individual (e.g. RNA-seq and ChIP-seq reads). For a SNP with heterozygous probability $H_{ik} = \min(0.99, H_{ik}^{\textrm{obs}})$, we define the updated heterozygous probability, $\hat{H}_{ik}$ as:  \[  \hat{H}_{ik} = \frac{H \Pr_{\mathrm{Bin}} \left( D \left| p=0.5 \right. \right)}  {H_{ik} \Pr_{\mathrm{Bin}} \left( D \left| p=0.5 \right. \right)  + (1 - H_{ik}) \left[ \Pr_{\mathrm{Bin}} \left( D \left| p=p_{err} \right. \right) + \Pr_{\mathrm{Bin}} \left( D \left| p=1-p_{err} p=1-p_{\textrm{err}}  \right. \right) \right]} \]  where $D$ represents the observed read count data and $p_{err}$ is the probability of a sequencing error.