Investigate negative-binomial mixture parameterizations that address component overlap

[fanshi118]

We want to look over papers / existing docs and find a methodical way to quantify the overlap / parametrize the distances between two Negative-Binomials. Such metrics as Hellinger distance and Bhattacharyya coefficient are potentially worth looking into.

This issue is related to #12 .

[fanshi118]

Found this paper…

[brandonwillard]

That's a pretty useful numerical study. The work they do to break down negative-binomials into Poisson-like terms might help with the derivation of a negative-binomial parameterization based on the standard additive Poisson parameterizations, but that would entail a bit of original research work.

Let's see if we can find papers with good examples of negative-binomial HMMs estimated with MCMC. These are likely to contain immediately useful parameterizations, prior choices, etc.

[fanshi118]

Okay, so far I've found this paper on total variation distance.

On the HMM / MCMC side, so far I haven't been able to find a lot of relevant docs specifically pertaining to parameterizations / prior choices for negative-binomials. Most of them tend to center around the applied use case of negative-binomial HMMs (i.e. RNA data, rainfall data).