Predictively Oriented Posteriors in PyMC

Standard Bayesian posteriors degrade under model misspecification by collapsing to point estimates. This project implements Predictively Oriented (PrO) posteriors in PyMC, a theoretically principled sampler that provides uncertainty calibrated to predictive reality rather than parameter estimation. The implementation includes a scoring-rule abstraction, Wasserstein gradient computation via PyTensor, vectorised particle simulation, and ArviZ integration with tutorials demonstrating robustness on real datasets.