[ENH] Add Bayesian modelling API PoC: base class, prior spec, ridge r…

[WHOIM1205]

Title

feat: add Bayesian modelling API (PoC) with Bayesian Ridge Regression

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Summary

This PR introduces a proof-of-concept Bayesian modelling layer to skpro, adding a consistent API for prior/posterior handling along with a working Bayesian Ridge Regression estimator.

The goal is to establish a foundation for integrating Bayesian workflows (priors, posterior inference, sequential updates) into the existing probabilistic framework without introducing new dependencies or breaking existing APIs.

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Changes

New

• _base.py

  • Adds BaseBayesianRegressor mixin extending BaseProbaRegressor
  • Introduces:
    • get_prior()
    • get_posterior()
    • get_posterior_summary()
    • sample_posterior()
    • update() for sequential learning

• _prior.py

  • Implements Prior abstraction
  • Wraps existing skpro distributions (no new DSL)
  • Backend-agnostic design

• _ridge.py

  • Adds BayesianRidgeRegressor
  • Closed-form posterior with Type-II ML (evidence maximization)
  • Supports sequential updates via sufficient statistics
  • Uses only numpy/scipy (no soft deps)

• tests/test_bayesian_ridge.py

  • 11 tests covering:
    • fit/predict behavior
    • posterior correctness
    • Bayesian API methods
    • sequential updates
    • prior validation

• README.md

  • PoC overview
  • Usage and run instructions

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Modified

• __init__.py
  • Export new Bayesian classes

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Test Plan

Run:

pytest skpro/regression/bayesian/tests/test_bayesian_ridge.py -v -o "addopts="