Unsupported Posterior Predictive Distributions

Suppose we want to use the geometric model with a beta prior which doesn't have a supported distribution for the posterior predictive.

from conjugate.distributions import Beta
from conjugate.models import geometric_beta

prior = Beta(1, 1)
posterior: Beta = geometric_beta(x_total=12, n=10, beta_prior=prior)

We can get posterior predictive samples by:

1. Sample from the posterior distribution
2. Sample from the model distribution using posterior samples

1. Using conjugate-models

This is easy to do with this package.

Since the distributions are vectorized, just:

1. Get the number of samples from the posterior
2. Take a single sample from the model distribution

from conjugate.distributions import Geometric

n_samples = 1_000
posterior_samples = posterior.dist.rvs(size=n_samples)
posterior_predictive_samples = Geometric(p=posterior_samples).dist.rvs()

2. Using pymc

Another route would be using PyMC then use the draw function.

import pymc as pm

posterior_dist = pm.Beta.dist(alpha=posterior.alpha, beta=posterior.beta)
geometric_posterior_predictive = pm.Geometric.dist(posterior_dist)

n_samples = 1_000
posterior_predictive_samples = pm.draw(geometric_posterior_predictive, draws=n_samples)

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