Finite-sample coverage of Bayesian-bootstrap calibration in SW-CRTs

Determine whether replacing the cluster-level resampling scheme with a Bayesian bootstrap that assigns Dirichlet weights to observed clusters can improve finite-sample coverage for calibrated Bayesian inference in stepped-wedge cluster-randomized trials.

Background

The paper’s calibrated variance procedure estimates sampling variability by resampling entire clusters, thereby preserving the stepped-wedge rollout and within-cluster dependence. The authors note that this resampling scheme could instead be replaced by a Bayesian bootstrap, which would assign Dirichlet weights to the observed clusters and keep the calibration procedure entirely within the Bayesian paradigm.

The theoretical justification established in the paper relies on resampled clusters being independent units. Because normalized Dirichlet weights would alter this structure, the proof would require modification. The unresolved issue is whether the Bayesian-bootstrap alternative would provide improved finite-sample frequentist coverage in stepped-wedge cluster-randomized trials.

References

Our cluster-level resampling scheme could be replaced by a Bayesian bootstrap, which places Dirichlet weights on the observed clusters rather than resampling them, and would keep the entire procedure within the Bayesian paradigm. Our proof of Theorem~\ref{calibrated_var_consistency} relies on the resampled clusters being independent units and would require modification under the normalized Dirichlet weights. Whether such an approach can also improve the finite-sample coverage in SW-CRTs remains an open question and will be explored in future research.

— Calibrated Bayesian inference for overall and subgroup-specific causal effects in stepped-wedge cluster-randomized trials  (2610.20858 - Liu et al., 14 Oct 2026) in Section Discussion, paragraph discussing Bayesian nonparametric working models and posterior calibration