Non-Parametric Estimation of the Posterior Distribution in Monitoring Primary School Enrollment in Mt. Elgon Region, Kenya
Wafula Elijah Sifuna *
Department of Mathematics, Kibabii University, Kenya.
Moses Kololi
Department of Mathematics, Kibabii University, Kenya.
John Sirengo
Department of Mathematics, Kibabii University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
This study presents an innovative Bayesian non-parametric framework for monitoring primary school enrollment in developing regions, with application to Kenya’s Mt. Elgon region. The study addresses critical limitations of conventional parametric methods through Bayesian Additive Regression Trees (BART), which captures complex enrollment patterns while providing probabilistic uncertainty quantification. Analyzing complete 2023 administrative data from all 53 public primary schools in the region, the approach reveals three key insights: research findings reveal near gender parity (51% boys, 49% girls) but significant disparities in Grade 2 and declining retention in middle grades (4–6). Secondly, the research identifies a concerning middle-grade attrition pattern with Grades 4-6 showing an 18% enrollment drop. Third, posterior distributions reveal stable enrollment clusters centered at 490 students per school (95% CI: 425-555). The model demonstrates strong predictive performance (RMSE = 188.52, MAE = 147.39) while outperforming conventional methods by 12-51% in accuracy metrics. These findings provide education planners with a robust decision-support tool for targeted resource allocation, particularly for addressing gender-specific retention challenges and middle-grade attrition. The methodology offers a scalable solution for educational monitoring in similar resource-constrained settings across sub-Saharan Africa.
Keywords: Bayesian nonparametrics, educational monitoring, BART, enrollment prediction, Kenya, primary education