JAX PathwaysCheck your starting point
Should an interval for a new noisy observation equal an interval for the latent mean prediction?
Compare your reasoning
No. The observation includes additional likelihood noise. Under the independent Gaussian model, add its variance to the latent predictive variance before taking a square root.
If this is unfamiliar, work through Build a Bayesian regression before attempting the project.
Build in stages
1. Build an exact reference
Keep distribution units and normalization, derive a posterior in a small solvable case and compare latent versus observation uncertainty.
2. Challenge approximate inference
Compare sampler moments with the exact target, inspect multiple-chain diagnostics and measure the covariance lost by a diagonal approximation. Use predictive residuals to challenge the likelihood itself.
Try a changed condition
Make a prediction before opening the reasoning. Keep your answer and the evidence you would collect.
Chains agree closely, but prediction residuals bend systematically with the input. What should be changed first?
Compare an approach
Investigate the model’s mean function and observation assumptions. Agreement between chains concerns exploration of the chosen posterior; it does not certify that the chosen model describes the data.
Diagnose a likely failure
Symptom: Intervals are narrow and diagnostics look reassuring despite poor predictions.
Check next: Check whether you plotted latent or observation uncertainty, and whether the likelihood or mean function misses structure.
Decide what is ready
Use bayesian-regression. Retain analytic posterior checks, sampler/approximation diagnostics and a predictive model-mismatch case, with uncertainty assumptions stated.
Where to put your project code
Write your code in: projects/bayesian-regression/my_model.py (copy projects/bayesian-regression/starter/model.py first: cp projects/bayesian-regression/starter/model.py projects/bayesian-regression/my_model.py).
Verify your implementation: python3 projects/bayesian-regression/tests/check.py --stage all --impl projects/bayesian-regression/my_model.py
Run the staged project checks on your implementation in projects/bayesian-regression/my_model.py and record your transfer experiment results in your portfolio.
What still needs further work
General hierarchical models and robust modern diagnostic workflows need further examples. The instructional sampler is not a replacement for validated inference libraries.