Variational dating does not allow a null mutation rate

[hyanwong]

For the other methods, we can ignore the mutations and simply estimate the branch lengths based on the prior. I'm not sure if this makes much sense for variational dating (and it might be poor for other dating too), but I simply note it here. If we don't allow it, we should explictly bomb out in variational_dates()

[nspope]

Hrm, I think it'd just reduce down to the iid prior if there's no mutation rate, because the Poisson likelihoods are undefined when $\mu = 0$ -- in which case, there's no approximation to compute (just the post-hoc correction to make branch lengths non-negative). So bombing out is the way to go.

[hyanwong]

Can we use this somehow to calculate a local prior from a global prior, though? Could we e.g. iterate while constraining the posterior of a parent to have a higher mean than its children, and run those messages around the graph?

[nspope]

Oh yes, I suppose even if the Poisson likelihood vanishes, there's still the parent > child indicator function. That'd need a separately designed EP algorithm to fit, though.