Naming of Likelihood Methods

[rmnldwg]

In a mixture model, there are two different likelihoods in use:

1. The incomplete likelihood we want to maximize. This marginalizes over the latent variables and thus does not require them
2. The complete likelihood which is much easier to compute and especially differentiate, but does require us to know/estimate the latent variables

In our model, we additionally want to compute the likelihoods of each patient under each mixture component, sometimes weighing them with the mixture coefficients and sometimes not.

So far, the result of these different likelihoods has been a mess of functions in the code. We currently have:

1. patient_component_likelihoods()
2. patient_mixture_likelihoods()
3. complete_data_likelihood()
4. incomplete_data_likelihood()

Each of them computable for slices/subsets of subgroups and components. But I think at least their names could be more informative. One could probably reduce this to two or three methods with appropriate names and a good choice of boolean flags (like use_complete or use_weighted).