Problem setting
Workflow starts before the model. A useful Bayesian analysis records assumptions, data-generating constraints, and the decision that the posterior will eventually inform.
The test problem is a weekly learning signal with sparse subgroups. The model must preserve uncertainty while remaining interpretable enough for revision.
Prior specification
A prior is treated as an auditable design choice. It states what would be surprising before data arrives and prevents weak observations from appearing stronger than they are.
Good workflow makes uncertainty visible early, not decorative at the end.
The first pass uses weakly regularizing assumptions. Tighter priors are introduced only when domain constraints can be written down and checked.
Diagnostics
Posterior predictive checks act as the main reading interface. The question is not whether the model is elegant, but whether simulated data resembles the observed process.
- Sampling health: convergence, effective sample size, and divergent transitions.
- Calibration: posterior predictive coverage across time and subgroup slices.
- Decision sensitivity: whether practical conclusions change under reasonable prior alternatives.
References
- Gelman, A. et al. Bayesian Data Analysis. CRC Press.
- McElreath, R. Statistical Rethinking. CRC Press.
- Vehtari, A., Gelman, A., and Gabry, J. Practical Bayesian model evaluation using leave-one-out cross-validation.