Dirichlet mixture of multinomials example (#18)

* Add a simple simulated-data example for DM distribution.

* Update DM example to conform to style-guide.

* Use InferenceData object for both posterior and ppc data storage.

* Update notebook workflow with new PPC code and null (multinomial) model.

* Big update to DM example text.

* Incorporate suggestions from @AlexAndorra, @ricardoV94, and @MarcoGorelli.

* Drop unused imports.

* Additional revisions suggested by @ricardoV94

* Clean up syntax of (dirichlet)multinomial explanation.

* More consistent variable names across simulation, models, text.

* Even fancier PPC plots.

* Additional minor revisions, TODOs.

* Revisions, also use forest-plots to examine accuracy of inferences.

* Fix some text and figures.

* Re-emphasize issues when NUTS fails.

Author: bsmith89

Diff for: examples/mixture_models/dirichlet_mixture_of_multinomials.ipynb

@@ -39,6 +39,7 @@ Gallery.contents = {
     "variational_inference/gaussian-mixture-model-advi": "Mixture Models",
     "mixture_models/gaussian_mixture_model": "Mixture Models",
     "mixture_models/marginalized_gaussian_mixture_model": "Mixture Models",
+    "mixture_models/dirichlet_mixture_of_multinomials": "Mixture Models",
     "samplers/SMC2_gaussians": "Simulation-based Inference",
     "samplers/SMC-ABC_Lotka-Volterra_example": "Simulation-based Inference",
     "survival_analysis/bayes_param_survival_pymc3": "Survival Analysis",