A Comparative Bayesian Hierarchical Model for Cost-Effectiveness in Uganda's Power-Distribution Equipment Systems (2000–2026)

{ "background": "The evaluation of cost-effectiveness in power-distribution infrastructure in developing economies is often hampered by sparse, heterogeneous data and the need to integrate expert judgement with observed performance metrics. Traditional deterministic models fail to adequately quantify uncertainty, which is critical for long-term investment planning.", "purpose and objectives": "This study develops and validates a novel comparative Bayesian hierarchical model to assess the cost-effectiveness of different equipment systems within a national power-distribution network. The objective is to provide a robust, probabilistic framework for ranking systems and informing capital allocation.", "methodology": "A comparative Bayesian hierarchical model was constructed, formalised as $y{ij} \\sim \\text{Normal}(\\thetaj, \\sigma^2), \\; \\thetaj \\sim \\text{Normal}(\\mu, \\tau^2)$, where $y{ij}$ represents cost-effectiveness observations for equipment type $j$, and $\\theta_j$ are the system-specific parameters pooled towards a global mean $\\mu$. The model integrates operational cost data, failure rates, and expert prior distributions on equipment longevity. Posterior distributions were computed using Markov chain Monte Carlo sampling.", "findings": "The model identified a clear hierarchy in system performance, with one equipment class demonstrating a 95% credible interval for cost-effectiveness superiority of [1.7, 3.2] relative to the lowest-ranked class. The analysis revealed that uncertainty in maintenance costs contributed over 60% of the total posterior predictive variance, highlighting a key risk driver.", "conclusion": "The Bayesian hierarchical framework provides a statistically rigorous method for comparative cost-effectiveness analysis under uncertainty, offering superior inference for decision-making compared to point-estimate approaches.", "recommendations": "Infrastructure planners should adopt probabilistic modelling to quantify investment risks. Future data collection should prioritise standardising maintenance cost reporting to reduce dominant uncertainty sources.", "key words": "Bayesian hierarchical model, cost-effectiveness analysis, power distribution, infrastructure investment, uncertainty quantification, developing economies", "contribution statement": "This paper