This study presents a comprehensive analysis of historical fire and climatic data to estimate the monthly frequency of vegetation fires in Kenya. This work introduces a statistical model that captures the behavior of fire count data, incorporating temporal explanatory factors and emphasizing the predictive significance of maximum temperature and rainfall. By employing Bayesian approaches, the paper integrates literature information, simulation studies, and real-world data to enhance model performance and generate more precise prediction intervals that encompass actual fire counts. To forecast monthly fire occurrences aggregated from the Moderate Resolution Imaging Spectroradiometer (MODIS) data in Kenya (2000-2018), the study utilizes maximum temperature and rainfall values derived from global GeoTiff (.tif) files sourced from the WorldClim database. The evaluation of the widely used Negative Binomial (NB) model and the proposed Bayesian Negative Binomial (BNB) model reveals the superiority of the latter in accounting for seasonal patterns and long-term trends. The simulation results demonstrate that the BNB model outperforms the NB model in terms of Root Mean Square Error (RMSE), and Mean Absolute Scaled Error (MASE) on both training and testing datasets. Furthermore, when applied to real data, the Bayesian Negative Binomial model exhibits better performance on the test dataset, showcasing lower RMSE (163.22 vs. 166.67), lower MASE (1.12 vs. 1.15), and reduced bias (-2.52% vs. -2.62%) compared to the NB model. The Bayesian model also offers prediction intervals that closely align with actual predictions, indicating its flexibility in forecasting the frequency of monthly fires. These findings underscore the importance of leveraging past data to forecast the future behavior of the fire regime, thus providing valuable insights for fire control strategies in Kenya. By integrating climatic factors and employing Bayesian modeling techniques, the study contributes to the understanding and prediction of vegetation fires, ultimately supporting proactive measures in mitigating their impact.
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