{"id":7378,"date":"2025-11-21T06:34:37","date_gmt":"2025-11-21T06:34:37","guid":{"rendered":"https:\/\/kibu.ac.ke\/sgs\/?p=7378"},"modified":"2025-11-21T06:35:47","modified_gmt":"2025-11-21T06:35:47","slug":"non-parametric-estimation-of-the-posterior-distribution-in-monitoring-primary-school-enrollment-in-mt-elgon-region-kenya","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/sgs\/non-parametric-estimation-of-the-posterior-distribution-in-monitoring-primary-school-enrollment-in-mt-elgon-region-kenya\/","title":{"rendered":"Non-Parametric Estimation of the Posterior Distribution in Monitoring Primary School Enrollment in Mt.Elgon Region, Kenya"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"7378\" class=\"elementor elementor-7378\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7a99c9ca elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7a99c9ca\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4f9410f8\" data-id=\"4f9410f8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1dd6941d elementor-section-content-bottom elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1dd6941d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-605d2cb2\" data-id=\"605d2cb2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-2c6ad1db\" data-id=\"2c6ad1db\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1271023e elementor-section-height-min-height elementor-section-items-stretch elementor-section-boxed elementor-section-height-default\" data-id=\"1271023e\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-49ce36df\" data-id=\"49ce36df\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-235a015a elementor-section-height-min-height elementor-section-content-middle elementor-section-boxed elementor-section-height-default\" data-id=\"235a015a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-72b4a278\" data-id=\"72b4a278\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6964138f elementor-widget elementor-widget-heading\" data-id=\"6964138f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Student\u2019s Name: <br>\nSifuna Elijah Wafula<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-1c610bb1\" data-id=\"1c610bb1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-347b8a11 elementor-widget elementor-widget-heading\" data-id=\"347b8a11\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Supervisors:<br>\n1.\tDr. Moses Kololi<br>\n2.\tDr. John Sirengo             \n\n<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-45e702d8\" data-id=\"45e702d8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4cbea754 elementor-widget elementor-widget-heading\" data-id=\"4cbea754\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Master of Science in Statistics<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-35fff4e2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"35fff4e2\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-7f268b05\" data-id=\"7f268b05\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-371d2508 elementor-widget elementor-widget-spacer\" data-id=\"371d2508\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-4d18d4fd\" data-id=\"4d18d4fd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-2f3d7e4c elementor-section-height-min-height elementor-section-boxed elementor-section-height-default\" data-id=\"2f3d7e4c\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-5881cb96\" data-id=\"5881cb96\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-137b0cc7 elementor-widget elementor-widget-heading\" data-id=\"137b0cc7\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">ABSTRACT<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-359569c6 elementor-widget elementor-widget-text-editor\" data-id=\"359569c6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Accurate monitoring of primary school enrollment is critical for educational planning in Kenya\u2019s 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\u2019 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\u2019s 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\u2019s 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.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-734dda71 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"734dda71\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1d27f397\" data-id=\"1d27f397\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Student\u2019s Name: Sifuna Elijah Wafula Supervisors: 1. Dr. Moses Kololi 2. Dr. John Sirengo Master of Science in Statistics ABSTRACT Accurate monitoring of primary school enrollment is critical for educational planning in Kenya\u2019s Mt. Elgon region, where parametric methods often fail to capture complex enrollment patterns due to their rigid assumptions. The problem of fluctuating [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-7378","post","type-post","status-publish","format-standard","hentry","category-theses"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Non-Parametric Estimation of the Posterior Distribution in Monitoring Primary School Enrollment in Mt.Elgon Region, Kenya - School of Graduate Studies<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/kibu.ac.ke\/sgs\/non-parametric-estimation-of-the-posterior-distribution-in-monitoring-primary-school-enrollment-in-mt-elgon-region-kenya\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Non-Parametric Estimation of the Posterior Distribution in Monitoring Primary School Enrollment in Mt.Elgon Region, Kenya - School of Graduate Studies\" \/>\n<meta property=\"og:description\" content=\"Student\u2019s Name: Sifuna Elijah Wafula Supervisors: 1. 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Dr. Moses Kololi 2. Dr. John Sirengo Master of Science in Statistics ABSTRACT Accurate monitoring of primary school enrollment is critical for educational planning in Kenya\u2019s Mt. Elgon region, where parametric methods often fail to capture complex enrollment patterns due to their rigid assumptions. 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