{ "background": "The assessment of industrial machinery adoption in developing economies often relies on aggregated statistics, which mask critical regional and sectoral heterogeneities. This methodological gap limits the diagnostic precision needed for targeted infrastructure and industrial policy.", "purpose and objectives": "This article presents a novel Bayesian hierarchical modelling framework designed to diagnose the adoption rates of industrial machinery fleets, capturing multi-level variability and providing probabilistic estimates for engineering and policy applications.", "methodology": "A three-level hierarchical model is developed, with machinery adoption status modelled as a Bernoulli outcome. The core structure is $y{ijk} \\sim \\text{Bernoulli}(\\theta{ijk}), \\; \\text{logit}(\\theta{ijk}) = \\alpha + ui + v{ij}$, where $ui$ and $v_{ij}$ are random effects for region and sector, with weakly informative priors. Inference is performed via Hamiltonian Monte Carlo to quantify uncertainty in adoption probabilities.", "findings": "The framework, applied to a synthetic dataset reflecting Tanzanian conditions, demonstrates that regional effects explain a substantial proportion (approximately 60%) of the variance in predicted adoption probabilities. Posterior distributions for sector-specific adoption rates show considerable uncertainty, with credible intervals spanning up to 0.4 probability units, highlighting the need for sub-national data granularity.", "conclusion": "The proposed Bayesian hierarchical model provides a robust, statistically coherent methodology for diagnosing machinery adoption, effectively quantifying uncertainty and disaggregating influences across administrative and industrial classifications.", "recommendations": "Adoption of this modelling approach is recommended for national engineering and planning bodies to generate nuanced diagnostics. Future work should integrate real-time telematics data to update the model's parameters dynamically.", "key words": "Bayesian inference, hierarchical model, adoption rate, industrial machinery, fleet management, probabilistic modelling, infrastructure diagnostics", "contribution statement": "This paper contributes a novel, generalisable modelling framework that formally quantifies uncertainty in adoption diagnostics, moving beyond point estimates to provide a full probabilistic assessment