Basic model assumptions and sampler tests

[brandonwillard]

We need to create some toy/example series and build tests around them. See the examples here for reference.

[brandonwillard]

FYI: I've created some toy model tests in a PR here.

[brandonwillard]

Here's a Gist that walks through the act of simulating and estimating the Poisson-Zero HMM model using the code in the .org file.

In general, we need to

• investigate different series lengths in order to make sure that performance doesn't degrade too much as the number of observations increases,
• make sure that estimation is consistent (statistically and performance-wise) for different ranges of parameter values (e.g. transition probabilities, Poisson rates)
• make sure that some basic posterior estimators (e.g. sample means and variances) are consistent with the simulated "true" values,
• perform all of the above under the FFBS and transition-matrix samplers (both independently and together),
• make sure that our samples will also work well in combination with other samplers (e.g. NUTS to estimate the Poisson rate)

[brandonwillard]

Now that we have a Python package set up, the results of this work should be additions to the unit tests in tests/.