Bayesian Modeling of INGARCHX Models for Cellulitis Related to Meteorological Factors in Mahasarakham and Roi-Et Hospitals

Abstract

The objective of this research is to develop integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models to represent the weekly incidence of cellulitis cases in relation to two exogenous variables: seasonality and the weekly average of either relative humidity or maximum temperature. The key to the proposed model is its capacity to explain overdispersion and lag dependence. For predictions and model parameters, we employ the Bayesian Markov Chain Monte Carlo (MCMC) approach, as supported by both a simulation study and an empirical study. To assess different models, we apply the deviance information criterion (DIC) criterion to the weekly cellulitis case sample data with two independent variables. In addition, we offer a one-week prediction to help Mahasarakham and Roi-Et Hospitals manage the increasing volume of hospital admissions by estimating the weekly cellulitis case incidence rate.