PHIE propagates uncertainty from HB domain posteriors to cross-tabulations via chi-square calibrated replicate weights, with tiered Calibrated Bayes intervals restoring near-nominal coverage and showing that uncertainty stems mainly from compositional sampling variability.
Small Area Estimation , 2nd edition
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Post-Hoc Inference of Cross-Classified Statistics from Hierarchical Bayes Survey Weights
PHIE propagates uncertainty from HB domain posteriors to cross-tabulations via chi-square calibrated replicate weights, with tiered Calibrated Bayes intervals restoring near-nominal coverage and showing that uncertainty stems mainly from compositional sampling variability.