Updating equations for the prior site type probabilities
We first derive the updating equations for the prior site type probabilities . The probability that the site is of type given that we observe the nucleotides in the reads at the site is:
Now, for we use our current value for , and if we further insert the expression for (25.3) we get:
We get the updating equation for the prior site type probabilities, , from equation 25.6: Let index the sites in the alignment (). Given the current values for the set of site frequencies, , and the current values for the set of error probabilities, we obtain updated values for the site frequencies, , by summing the site type probabilities given the data (as given by equation 25.6) across all sites in the alignment: