Calculate Founders More Accuately

[reedacartwright]

Currently dng-call assumes that all founders are samples from independent populations govern by identical finite-sites models. This simplifies our peeling calculations. However, they should all come from the same population and be dependent samples:

P(g_i | g_1 ... g_{i-1}; params) ~ DirichletMultinomial(params, g_1 ... g_{i-1})

There are many ways to improve probability calculations after a site has been found to be a candidate:

• Estimate the allele frequency at that site in the founders and calculating probabilities using that.
• Numerically integrate or sample over possible allele frequencies. Because individuals are independent once allele frequencies are known.
• Use Gibbs sampling to evaluate the the expectation
• If two parents are founders, sample correctly their joint frequency.

Determine which one of these to do.