Probabilistic Temperature-Profile Retrieval from Crowdsourced Smartphone Pressure Sensors: Hierarchical Bayesian Bias Correction and Coverage Equity for Urban Heat Analytics

Crowdsourced smartphone pressure sensors offer dense urban coverage but their use for temperature-profile retrieval is complicated by device heterogeneity, unknown sampling heights, and non-random participation that concentrates observations in affluent, well-instrumented districts. The framework is evaluated through a replication-based replication study in which 600 data sets of N = 500 were drawn from a declared data-generating process with intercept 12.0, exposure 0.42, group -3.1, severity 1.35, and error SD 4.2, and the ordinary least squares estimator was characterised under that process. Across the 600 replications, estimated bias was -0.04793 for the intercept and 0.00104 for the exposure coefficient, with RMSE of 0.8839 and 0.01612 respectively, and empirical coverage of the nominal 95% confidence intervals was 1.0 for both parameters. The results indicate that the estimator is approximately unbiased for the exposure coefficient but exhibits small negative intercept bias, and that nominal intervals are conservative under the stated process. Coverage equity should be treated as a design constraint on sensor-network analytics rather than a post hoc diagnostic, and it specifies the conditions under which hierarchical bias correction preserves both retrieval accuracy and distributional fairness in urban heat mapping.