{ "background": "Evaluating the efficiency of community health centres is critical for improving service delivery in resource-constrained settings. Existing methods often fail to account for unobserved heterogeneity and the hierarchical structure of health system data, leading to biased estimates of operational performance.", "purpose and objectives": "This study presents and evaluates a novel Bayesian hierarchical model designed to measure efficiency gains within community-based healthcare systems. The objective is to provide a robust methodological framework that quantifies centre-level efficiency while formally incorporating uncertainty.", "methodology": "We developed a Bayesian stochastic frontier model with a hierarchical structure: $\\ln(y{ij}) = \\beta0 + \\mathbf{X}{ij}\\beta + v{ij} - u{ij}$, where $u{ij} \\sim \\text{Half-Normal}^{+}(0, \\sigmau^2)$ represents inefficiency, $v{ij}$ is noise, and random effects capture centre-level clustering. The model was applied to a panel dataset of Tanzanian community health centres, incorporating inputs (staff, equipment) and outputs (patient visits, vaccinations). Inference used Markov chain Monte Carlo sampling.", "findings": "The model identified significant variation in technical efficiency across centres, with a posterior median efficiency score of 0.72 (95% credible interval: 0.68 to 0.76). This indicates that, on average, centres could potentially increase output by 28% using existing resources. The hierarchical structure improved model fit, with the Watanabe-Akaike information criterion decreasing by over 15 points compared to a non-hierarchical specification.", "conclusion": "The proposed Bayesian hierarchical model offers a statistically rigorous tool for efficiency analysis in complex health systems, providing a fuller quantification of uncertainty through posterior distributions.", "recommendations": "Health policymakers should adopt hierarchical modelling techniques for performance assessment to better identify underperforming units and allocate resources. Future research should integrate contextual environmental factors into the efficiency frontier.", "key words": "health systems efficiency, stochastic frontier analysis, Bayesian statistics,