Bayesian Modeling of Zero-Inflated Count Time Series Using Adaptive MCMC on Dengue Incidence of Iligan and Tandag City, Philippines

Abstract

This study presents a Bayesian approach to modeling dengue incidence in Iligan and Tandag cities in the Philippines using integer-valued time series models. Recognizing the challenges posed by overdispersion, serial dependence, and excess zeros in dengue count data, we compare five probabilistic models: Generalized Poisson (GP), Log-Generalized Poisson (Log-GP), Negative Binomial (NB), Zero-Inflated Generalized Poisson (ZIGP), and Zero-Inflated Negative Binomial (ZINB) INGARCHX models. These models incorporate rainfall and temperature as lagged exogenous covariates. Parameter estimation is carried out using Adaptive Markov Chain Monte Carlo (MCMC) methods, and model performance is assessed via the Deviance Information Criterion (DIC) and residual diagnostics. Results reveal that the ZINB-INGARCHX model is best suited for the zero-inflated Tandag dataset, while the ZIGP-INGARCHX model provides the best fit for the overdispersed Iligan data. Findings highlight the importance of flexible count models and lagged environmental drivers in accurately capturing the dynamics of dengue transmission.