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\subsection{Estimating overdispersion parameters}  In order to estimate the genome-wide overdispersion parameters $\Phi_i$ and $\Upsilon_i$, we use the same likelihood equations as in the CHT, but assume that there are no genetic effects. This means that for the read depth part of the test the mean estimate, $\lambda$, is equal to the expected counts, $T^*_{ij}. $T^*_{ij}$.  For the allele specific part of the test, $p$ is equal to $0.5$. The fraction of reads comSince the allele specific and read depth parts of the likelihood equation are independent, we can fit the overdispersion parameters separately. \subsubsection{Beta-Negative-Binomial}