Non-Parametric Estimation of the Posterior Distribution in Monitoring Primary School Enrollment in Mt.Elgon Region, Kenya

Accurate monitoring of primary school enrollment is critical for educational planning in Kenya’s Mt. Elgon region, where parametric methods often fail to capture complex enrollment patterns due to their rigid assumptions. The problem of fluctuating enrollment poses significant challenges for educational planners and policymakers in effectively allocating resources and ensuring consistent access to education, as existing parametric techniques fail to comprehensively capture enrollment trends due to their limitations in handling complex non-linear relationships. The study used a non-parametric approach using Bayesian Additive Regression Trees (BART) to overcome these limitations. The specific objectives were to use exploratory data analysis of learners enrollment records, apply Bayesian Additive Regression Tree in estimating learners’ enrollment, and estimation of the posterior distribution using Bayesian Additive Regression Tree. BART effectively handles complex datasets through its combination of non-parametric methods and Bayesian inference, making it particularly suitable for modeling educational enrollment patterns with inherent non-linearities and interactions. The methodology employed a comprehensive analytical framework beginning with exploratory data analysis of 2023 enrollment records from 53 primary schools in the region. This preliminary examination identified baseline patterns across grades, gender, and school sizes. The analysis utilized BART with 200 decision trees and Markov Chain Monte Carlo sampling for posterior estimation, incorporating rigorous multicollinearity checks to ensure robust variable selection. The model’s performance was evaluated using standard metrics including Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). Key findings revealed several important insights: while overall gender parity was maintained (51% boys, 49% girls), significant disparities emerged in Grade 2. The analysis identified concerning retention patterns, with marked enrollment declines in middle grades (4-6), and substantial variations in school sizes ranging from 200 to over 1,000 learners. The BART model demonstrated strong predictive performance with RMSE of 188.5167 and MAE of 147.3871, while posterior distributions revealed stable enrollment clusters around 490 learners per school. These results suggest three priority policy interventions: targeted programs to address middle-grade attrition, gender-specific initiatives in early primary years, and differentiated resource allocation based on school size variations. The study confirms BART’s effectiveness as a monitoring tool that better captures enrollment complexities than conventional methods. The approach provides education planners with a flexible, evidence-based framework for decision-making, offering significant potential for improving educational access and resource efficiency in similar developing regions facing enrollment monitoring challenges.