Expose Laplace Approximation

[charlesm93]

Summary:

Complements issue 755 in the math repo.

Description:

The goal is to design specialized functions to efficiently compute the posteriors of latent gaussian models. In particular we want to consider the case where the observations follow a conditional distribution which is Normal, Poisson, Binomial, and Negative Binomial.

Exposing the functions shouldn't be too hard, as at first glance the functions are not higher-order functions. This may change if we make the functions less specialized and more flexible.

Current Version:

v2.17.1

[bob-carpenter]

@charlesm93 --- thanks for following up on this. Could you include the specific signatures you're proposing either here or in the math lib issue?

I'd strongly suggest tackling one of these functions end-to-end first. At that point, the others should be easy to knock out or delegate.

[charlesm93]

@bob-carpenter Yes, I'll get to it, though not in the immediate future. We still need a good proof of concept and tests to asses how efficacious the approximation is. But right now, I don't have time to get to it.