Step 6 - Posterior Predictive Distribution

Notation

For each posterior draw of $(\mu_i, \sigma_i)$ from Step 3, simulate a score $z_i \sim \text{Normal}(\mu_i, \sigma_i)$. The resulting spread of simulated scores, across all the draws, is the score-level distribution that folds in parameter uncertainty — the Bayesian analogue of classical's fitted normal, but built from a whole posterior of plausible $(\mu_i, \sigma_i)$ pairs rather than a single point estimate of each. (The closed-form conjugate route would instead give this analytically as a Student-t.)

step 1 - draw posterior predictive samples

(to be added)

step 2 - plot the posterior predictive distributions

(to be added)

Python

filename: step6_posterior_predictive.py