Changes

Hardy Weinberg equilibrium is expected in a panmictic population.  The following formulation is a likelihood ratio test statistic that incorporates the genotype uncertainty via genotype likelihoods.  

Hardy Weinberg equilibrium is expected in a panmictic population.  The following formulation is a likelihood ratio test statistic that incorporates genotype uncertainty via genotype likelihoods.  

<math>P(R_{k}|\textbf{p})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus observes HWE.  

<math>P(R_{k}|\textbf{p})</math> is the probability of observing the reads for individual <math>k</math> assuming that a locus observes HWE.  

<math>P(R_{k}|\textbf{g})</math>  is the probability of observing the reads for individual <math>k</math> assuming that a locus does not observe HWE.

<math>P(R_{k}|\textbf{g})</math>  is the probability of observing the reads for individual <math>k</math> assuming that a locus does not observe HWE.

<math>

<math>

\begin{align}

\begin{align}

   L(R|g) & =  & \frac{\prod_{k}{P(R_{k}|\textbf{p})}}

   L(R|g) & =  \frac{\prod_{k}{P(R_{k}|\textbf{p})}}

                     {\prod_{k}{P(R_{k}|\textbf{g})}} \\

                     {\prod_{k}{P(R_{k}|\textbf{g})}} \\

         & = & \frac{\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}|\textbf{p})}}}

         & =   \frac{\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}|\textbf{p})}}}

                     {\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}|\textbf{g})}}} \\

                     {\prod_{k}{\sum_{i,j}{P(R_{k}, G_{i,j}|\textbf{g})}}} \\

         & = & \frac{\prod_{k}{\sum_{i,j}{P(R_{k} |G_{i,j} )P(G_{i,j}|\textbf{p})}}}

         & =   \frac{\prod_{k}{\sum_{i,j}{P(R_{k} |G_{i,j} )P(G_{i,j}|\textbf{p})}}}

                     {\prod_{k}{\sum_{i,j}{P(R_{k} |G_{i,j})P(G_{i,j}|\textbf{g})}}} \\

                     {\prod_{k}{\sum_{i,j}{P(R_{k} |G_{i,j})P(G_{i,j}|\textbf{g})}}} \\

\end{align}

\end{align}