Bayesian Conditional Autoregressive for Rainfall Modeling in East Java

Rainfall in East Java has high spatial variation, requiring a modeling approach that can capture inter-regional dependencies. This study aims to estimate rainfall patterns using Bayesian Conditional Autoregressive (BCAR) models that incorporate spatial effects, specifically the Intrinsic Conditional Autoregressive (ICAR) and Leroux CAR specifications. Parameter estimation was conducted using Markov Chain Monte Carlo (MCMC) methods to ensure convergence and posterior stability. Monthly rainfall data from East Java during the 2022–2023 were analyzed by dividing the period into the transition to the rainy season (September–November) and the rainy season (December–February). The results indicate that during the rainy season, most climatic variables, including temperature, humidity, wind direstion, and cloud cover, do not show statistically significant effects on rainfall, whereas during the transition season,wind exhibits a significant positive influence. Comparative model evaluation reveals that the ICAR model provides the best predictive performance, as indicated by the lowest Root Mean Square Error (RMSE), while the Leroux CAR model demonstrates consistent estimation of spatial dependence across both periods. Simulation results further confirm that the parameter estimators are unbiased, as evidenced by the close agreement between simulated parameters and empirical data estimates. These findings demonstrate that BCAR models, particularly the ICAR specification, are effective in capturing spatial rainfall variability in East Java. This study contributes methodologically to spatial climatological analysis and provides a foundation for future research incorporating additional covariates and extended temporal coverage to enhance rainfall prediction accuracy.