A Bayesian Hierarchical Modelling Framework for Evaluating Process-Control System Adoption in Tanzania (2000–2026)

"background": "The adoption of modern process-control systems in engineering sectors is critical for industrial development, yet robust methodologies for evaluating adoption rates and their drivers are lacking. Existing approaches often rely on cross-sectional surveys or deterministic models, which fail to account for hierarchical data structures and inherent uncertainties in longitudinal adoption processes. ", "purpose and objectives": "This article presents a novel Bayesian hierarchical modelling framework designed to quantify the adoption rates of process-control systems and to identify key technical and organisational factors influencing adoption. The objective is to provide a rigorous, probabilistic methodology that can handle sparse or incomplete data typical in such contexts. ", "methodology": "A three-level hierarchical model is developed, where the adoption status of a system for a given project i in region j at time t is modelled as y{ijt \ (), with () = \ + \ Xijt. Region-specific intercepts \ are drawn from a common normal distribution, \ \ N (\\, \²_\), allowing partial pooling of information across regions. Inference is performed using Hamiltonian Monte Carlo, with posterior distributions summarising all parameter and prediction uncertainty. ", "findings": "The framework's application to a simulated dataset, constructed from expert elicitation, demonstrates its utility. A key finding is the model's ability to produce probabilistically coherent estimates, such as a posterior median for the national-level adoption growth parameter of 0. 15 per annum, with a 90% credible interval of 0. 08, 0. 22, indicating a positive but uncertain trajectory. The hierarchical structure reveals substantial regional heterogeneity in baseline adoption probabilities. ", "conclusion": "The proposed Bayesian hierarchical model provides a statistically sound and flexible methodology for evaluating technology adoption in engineering. It formally incorporates multi-level variability and quantifies uncertainty in estimates and predictions, offering a superior