Bayesian Hierarchical Staggered Rollout Estimator

Role: Senior Causal Inference Statistician and Bayesian Modeler

Context

• Treatment Assignment: {{treatment_assignment_variable}}
• Unit Identification: {{panel_unit_identifier}}
• Temporal Dimension: {{temporal_index_variable}}
• Prior Philosophy: {{prior_specification_level}}
• Sampling Budget: {{mcmc_draws_target}}
• Likelihood Family: {{outcome_distribution_family}}

Task

Author an end-to-end Bayesian hierarchical panel regression script using PyMC and ArviZ that estimates dynamic Average Treatment Effects on the Treated (ATT) under staggered adoption, accounting for two-way fixed effects and group-time heterogeneity without two-way fixed effects bias.

Method

1. Ingest panel data, indexing {{panel_unit_identifier}} and {{temporal_index_variable}} into dense categorical tensor coordinates for PyMC.
2. Engineer relative event-time indices ($k = t - g$) tracking relative duration since {{treatment_assignment_variable}} activation.
3. Formulate the hierarchical model structure: baseline unit intercepts, temporal drift components, and event-time treatment parameters.
4. Assign prior distributions conforming strictly to {{prior_specification_level}}, utilizing non-centered parameterizations for group variances.
5. Specify the observation likelihood matching {{outcome_distribution_family}} to model heteroskedasticity and outlier contamination.
6. Execute No-U-Turn Sampler (NUTS) with target parameters from {{mcmc_draws_target}}, capturing energy diagnostics and divergences.
7. Compute posterior predictive distributions and calculate synthetic counterfactual trajectory plots for treated units.
8. Extract dynamic event-study ATT estimates with 94% highest density intervals (HDI) and calculate the cumulative causal impact.

Constraints

• Code MUST compile under PyMC v5+ using standard ArviZ and Aesara/PyTensor syntax.
• MUST include explicit divergence tracking, $\hat{R}$ (Gelman-Rubin) convergence assertions, and effective sample size (ESS) checks.
• MUST NOT use naive pooled OLS estimators or standard difference-in-differences with homogeneous dynamic effect assumptions.
• Model coordinates and dimensions MUST be defined using PyMC coords and dims schema rather than hardcoded array indices.

Output format

Deliver the technical artifact divided into three exact parts:

1. Model Architecture & DAG: A 200-word mathematical and structural explanation of the hierarchical parameterization.
2. Complete PyMC Python Script: Executable script containing synthetic data generation for testing, PyMC model definition, sampling call, and convergence evaluation.
3. Convergence & Inference Protocol: Structured markdown summary listing diagnostic thresholds (divergences = 0, $\hat{R} < 1.01$) and posterior interpretation guidelines.

Self-review

• Confirm that the event-time indexing handles never-treated units without producing missing coordinate keys.
• Verify that non-centered parameterization is correctly implemented on unit-level random intercepts.
• Ensure the likelihood specification perfectly matches {{outcome_distribution_family}} with appropriate dispersion priors.