basic posterior-predictive checks

[jburos]

It would be nice to facilitate basic posterior predictive checks.

A simplified version of this will take two inputs :

1. a matrix of simulated values (y_reps) from the model, dimensions N*S where
   • N = number observations and
   • S = posterior simulations/draws
2. a vector of observed data (y + optional covariates) from the data, of dimensions N*X where
   • X = number of covariates

An enhanced version takes a summary function to apply to the posterior values, such as "min", 10th percentile, etc.

Idea is to support/streamline the following tasks :

1. plotting distribution of observed data vs sampled draws from the posterior
2. optionally plot distribution of observed data according to values of covariates
3. optionally apply the function to the observed data, plot distribution of summary statistic over posterior draws in context of observed value
   • in this case, summarize similarity of test statistic vs the posterior draws using classical statistics test: How likely to see observed value if the distribution sampled from the model were true?