A Hybrid Statistical and Probabilistic Model for Forecasting Uncertain Events

Abstract

Forecasting uncertain events requires models that provide more than a single expected value, particularly when the target is a variable event count affected by seasonality, environmental conditions, and irregular outbreak peaks. This study proposes and evaluates a hybrid statistical-probabilistic framework for forecasting uncertain events, using weekly dengue incidence as an empirical case study. The framework integrates time-series structuring, lagged statistical features, environmental regression predictors, ensemble point forecasting, negative-binomial distribution fitting, and uncertainty interval estimation. A public dengue forecasting dataset containing 1,456 city-week observations from San Juan and Iquitos was used for chronological model evaluation. The proposed model was compared with seasonal naive, moving-average, log-ridge regression, random-forest, and gradient-boosting baselines using mean absolute error (MAE), root mean squared error (RMSE), symmetric mean absolute percentage error, prediction-interval coverage, and interval width. The hybrid model achieved the lowest validation error, with an MAE of 5.908 and an RMSE of 9.874, outperforming the seasonal naive baseline by a large margin and modestly improving over the individual ensemble learners. The probabilistic layer produced empirically conservative uncertainty intervals, with 87.67% coverage for the nominal 80% interval and 93.84% coverage for the nominal 90% interval. Feature-importance results showed that recent case history was the strongest predictor, while precipitation, temperature, humidity, and time-index variables contributed additional contextual information. The study contributes an interpretable forecasting framework that connects statistical temporal structure with probabilistic event-risk estimation. The main limitation is that the empirical evidence is based on two locations, so future research should test the framework across broader domains of outbreak, climate, financial, and operational events.