{ "background": "Community health centres in Nigeria face persistent challenges in optimising the yield of medical services and interventions from limited resources. Existing evaluation frameworks often lack the statistical rigour to account for hierarchical data structures and inherent uncertainty in performance measurement.", "purpose and objectives": "This case study presents and methodologically evaluates a Bayesian hierarchical model designed to measure and optimise service yield within these centres. The primary objective is to demonstrate the model's utility for robust inference and its capacity to inform resource allocation.", "methodology": "We developed a Bayesian hierarchical model where the log-transformed yield $\\log(y{ij}) = \\alpha + \\beta X{ij} + uj + \\epsilon{ij}$ for centre $j$ and observation $i$, with $uj \\sim N(0, \\sigmau^2)$ representing centre-level random effects. The model was applied to synthetically generated data reflecting typical centre operations, with posterior distributions estimated using Markov chain Monte Carlo sampling.", "findings": "The model successfully quantified uncertainty in yield estimates, with the 95% credible interval for the key resource allocation coefficient excluding zero, indicating a statistically meaningful relationship. A principal finding was that a hypothetical reallocation of nursing staff, informed by the model's posterior predictions, was associated with a potential yield improvement of approximately 15% in a simulated intervention scenario.", "conclusion": "The Bayesian hierarchical approach provides a statistically robust framework for analysing yield data from community health systems, effectively handling multi-level data and propagating uncertainty to final estimates.", "recommendations": "Health systems researchers should adopt hierarchical modelling techniques to account for clustering in centre-level data. Programme managers could utilise such models for piloting resource reallocation strategies before wide-scale implementation.", "key words": "Bayesian inference, health systems research, resource allocation, hierarchical modelling, sub-Saharan Africa", "contribution statement": "This study provides a novel methodological framework for health systems yield analysis, demonstrating through a case study how Bayesian hierarchical models can generate actionable,