Abstract
{ "background": "Evaluating the cost-effectiveness of water treatment systems in developing regions is critical for sustainable infrastructure investment. Current diagnostic methods often lack the ability to formally incorporate operational variability and uncertainty, leading to suboptimal resource allocation.", "purpose and objectives": "This study develops and applies a novel Bayesian hierarchical model to diagnose the cost-effectiveness of diverse water treatment facilities. The objective is to provide a robust, probabilistic framework for comparing system performance while quantifying uncertainty in key economic and engineering parameters.", "methodology": "A Bayesian hierarchical model was constructed, integrating cost data and technical performance indicators from a sample of treatment systems. The core model structure is $\\text{log}(\\text{Cost}{ij}) = \\alphaj + \\beta X{ij} + \\epsilon{ij}$, with $\\alphaj \\sim \\text{Normal}(\\mu\\alpha, \\sigma^2_\\alpha)$, where $i$ indexes facilities and $j$ indexes system types. Parameters were estimated using Hamiltonian Monte Carlo sampling.", "findings": "The model identified substantial heterogeneity in cost-effectiveness across system types. Slow sand filtration systems demonstrated a 95% credible interval for normalised cost per cubic metre of [TZS 120, TZS 185], which was significantly lower and more predictable than for mechanised systems. The posterior probability that community-managed schemes are more cost-effective than centrally managed ones exceeded 0.85.", "conclusion": "The Bayesian hierarchical framework provides a superior diagnostic tool for infrastructure investment by explicitly modelling uncertainty and variability. It reveals that non-mechanised, locally managed systems frequently offer more predictable and favourable cost-effectiveness profiles in this context.", "recommendations": "Infrastructure planners should adopt probabilistic, hierarchical modelling for comparative system analyses. Investment should prioritise system types with tighter credible intervals for cost-effectiveness, enhancing financial risk management. Further data collection should standardise the reporting of operational and maintenance costs.", "key words": "Bayesian inference, infrastructure economics, water treatment, cost-benefit analysis