{ "background": "Community health centres are critical for healthcare delivery in Rwanda, yet systematic methodologies for quantifying and optimising their operational yield remain underdeveloped. Yield, defined as the effective utilisation of resources to achieve health outcomes, requires robust statistical frameworks for measurement and improvement.", "purpose and objectives": "This systematic review evaluates the application of Bayesian hierarchical modelling methodologies for yield optimisation within Rwanda's community health centre systems. It aims to synthesise methodological approaches, assess model efficacy, and identify gaps in current research.", "methodology": "A systematic search of multiple electronic databases was conducted following PRISMA guidelines. Studies were included if they employed Bayesian hierarchical models to analyse health system performance or resource optimisation. Data were extracted on model specification, prior selection, computational techniques, and validation metrics. The core model form reviewed is $y{ij} \\sim \\text{Normal}(\\alphaj + X{ij}\\beta, \\sigma^2), \\; \\alphaj \\sim \\text{Normal}(\\mu{\\alpha}, \\tau^2)$, where $y{ij}$ is the yield outcome for centre $j$, with partial pooling of centre-level effects $\\alpha_j$.", "findings": "The review identified a predominant theme: models incorporating spatial random effects and informative priors from expert knowledge significantly improved yield estimates, reducing posterior credible interval width by approximately 30% compared to non-hierical models. However, a critical gap was the frequent lack of model checking using posterior predictive distributions.", "conclusion": "Bayesian hierarchical modelling offers a powerful, flexible framework for analysing yield in complex, nested health systems, facilitating evidence-based resource allocation. Its adoption in this context is nascent but methodologically promising.", "recommendations": "Future research should prioritise the development of integrated models that combine operational, clinical, and spatial data. Practitioners should adopt robust model validation practices, including sensitivity analyses to prior specifications.", "key words": "Bayesian inference, health systems research, resource allocation, partial pooling, sub