Bayesian Logistic Regression for Inhomogeneous Poisson Point Process: A Case Study of Post-Harvest Facilities in Sidenreng Rappang - Husain, Ahmad; Sam, Marwan; Jamaluddin, Sri Rezki Wahdania (JTAM (Jurnal Teori dan Aplikasi Matematika), 2026)
Understanding the spatial distribution of post-harvest infrastructure is crucial for improving the efficiency and resilience of agricultural supply chains, particularly in major food-producing regions. This study aims to extend the estimating equations based on the logistic regression likelihood within the Bayesian framework to model the spatial intensity of an Inhomogeneous Poisson Point Process (IPP). The proposed approach integrates prior information into the logistic regression likelihood by constructing posterior distributions, enabling a more comprehensive inference by quantifying parameter uncertainty. In contrast to conventional maximum likelihood (ML) estimation, which produces only point estimates, the Bayesian method provides a probabilistic characterization of parameter estimates using the Markov Chain Monte Carlo (MCMC) approach, specifically the Gibbs Sampling algorithm, to approximate posterior distributions. The methodological framework is applied to the spatial distribution of post-harvest rice facilities in Sidenreng Rappang Regency, Indonesia. The analysis is based on georeferenced observational data obtained from local goverment records and agricultural statistics, processed usign Geographic Information System (GIS) tools and statistical software. Spatial covariates include the proportion of paddy field area per village (Z_1), rice producing area (Z_2), and distance to the nearest Bulog warehouse (Z_3 ). The results indicate that Z₁ and Z₃ significantly affect the spatial intensity of post-harvest facilities, where areas with larger paddy field proportions are more likely to host such facilities, while increasing distance from Bulog reduces the likelihood of facility presence. The posterior trace and density plots demonstrate good convergence and mixing, confirming the reliability of the Gibbs Sampling procedure. Model comparison through the Akaike Information Criterion (AIC) and likelihood values shows that the Bayesian approach yields a substantially lower AIC, ten times smaller than the ML-based logistic regression, indicating superior model fit and computational efficiency. The findings suggest that integrating Bayesian inference into the IPP logistic framework enhances model interpretability and robustness, particularly in accounting for uncertainty and prior knowledge. The study underscores the practical importance of spatial modeling for agricultural infrastructure planning and offers a flexible computational framework applicable to other spatial point pattern analyses across diverse domains.