Generative model of coverage for germline

[davidbenjamin]

Generative models with the raw data as an observed node have many advantages over approaches in which the raw data is pre-processed. We would like a generative model relating observed read counts to hidden copy number state.

This will be easiest to try first on our germline code, for two significant reasons:

• There are finitely many hidden states because cell fractions and purity don't enter
• We already have a lot of probabilistic graphical model machinery set up in the form of an HMM for segmentation and calling. A new emission likelihood model can be swapped into the HMM in a completely modular manner.

If this succeeds, it would then not be so hard to surmount those obstacle for somatic calling, but there is no good reason not to do the simpler thing first.

[davidbenjamin]

Note: this will close issue #371 (fast PCA) because probabilistic PCA models are best learned via a fast EM algorithm.

[davidbenjamin]

Note: this is able to issue #381 (deal with copy number events in the panel of normals / cohort) because if copy ratio / copy number is part of the generative model then learning the parameters of the model will take that into account.

[davidbenjamin]

Closed by PR #416. Now there are several tickets for the implementation.