Quantifying the Threat: A Bayesian Probabilistic Framework for Heavy Metal Health Risks among Children in the Densu Basin, Ghana

Abstract

Groundwater in Ghana's Densu River Basin remains a key domestic water source, but multi-metal contamination threatens children's health. Previous deterministic hazard index assessments provide limited treatment of uncertainty, co-exposure, and spatial variability. This study applies a Bayesian probabilistic framework for non-carcinogenic risk assessment using 94 groundwater samples and measurements of Fe, Mn, Ni, Pb, Cd, and As. A Bayesian regression model propagates parameter uncertainty and accounts for contaminant co-occurrence. Adaptive Hamiltonian Monte Carlo is used for posterior inference, while inverse distance weighting generates spatially continuous risk surfaces. Pb, As, and Cd dominate cumulative risk. Posterior predictive results indicate that approximately 31% of sampling sites have a probability greater than 0.5 of exceeding a hazard index (HI) of 1. The risk surface is highly heterogeneous, with a posterior mean of 0.372 and a standard deviation of 0.416. High-risk zones often reflect moderate co-exposure rather than extreme contamination by a single metal. The framework provides uncertainty-aware, spatially explicit information to support groundwater monitoring, risk mitigation, and public health planning in data-limited regions.