support for essential log density functions

[dustinvtran]

Discrete

• [x] Bernoulli
• [x] Binomial
• [x] Multinomial
• [x] Poisson
• [x] Geometric
• [x] Negative Binomial

Continuous

• [x] Uniform
• [x] Multivariate Normal
• [x] Student-t (with mean and scale parameters)
• [x] Gamma
• [x] Inverse Gamma
• [x] Exponential
• [x] Beta
• [x] Dirichlet
• [x] Log-Normal
• [x] Chi-squared

useful references:

• https://github.com/GPflow/GPflow/blob/master/GPflow/densities.py
• https://github.com/davmre/bayesflow/blob/master/bayesflow/dists.py
• https://github.com/scipy/scipy/blob/0ed06d74a3cf28af9efcedd1f8bcc928066975bb/scipy/stats/_multivariate.py

[dustinvtran]

@altosaar writes:

also forgot to mention - instead of re-coding e.g. gamma variables in tensorflow, why not write kernels for them in c++ and then bazel compile? then you could just wrap stan math for distributions?!

Also a possibility!

[dustinvtran]

The dirichlet log pdf has a bug and I think the multinomial and gamma/inverse gamma distributions do too. I'll fix this in a branch now with some basic unit tests.