hybrid probabilistic forecasting

This study addresses the limitation of existing forecasting systems that rely predominantly on point predictions and thus fail to adequately characterize uncertainty for informed decision-making. To overcome this, the authors propose a hybrid framework that extends point forecasts from classical models—such as Theta, exponential smoothing, and ARIMA—into probabilistic forecasts by integrating error post-processing with model-specific, horizon-dependent uncertainty scaling. The approach calibrates forecast errors using historical simulation, conformal prediction, quantile regression, and GARCH-based methods, and systematically evaluates in-sample versus out-of-sample calibration performance. Empirical results on the M4 dataset demonstrate an average 4.6% reduction in Continuous Ranked Probability Score (CRPS). In-sample calibration consistently outperforms out-of-sample calibration, particularly over longer forecast horizons, thereby validating the effectiveness and practical utility of the proposed framework.

Probabilistic forecasting in dynamical systems remains challenging due to missing data and observational noise, which hinder reliable uncertainty quantification. Method: We propose an end-to-end learning framework integrating stochastic differential equation (SDE) modeling, Bayesian inference, and variational approximation—introducing stochastic interpolation to probabilistic forecasting for the first time, enabling distributional (rather than point) predictions of future states. Our approach explicitly encodes physical priors from dynamical systems theory, ensuring both theoretical interpretability and robustness to incomplete and noisy observations. Results: Evaluated on multiple benchmarks including WeatherBench, our method improves prediction interval coverage and calibration by over 25% compared to deterministic baselines. It establishes a novel paradigm for long-horizon uncertainty quantification in meteorological and physics-informed modeling.

Malaria forecasting in sub-Saharan Africa faces significant challenges due to strong seasonality, reporting biases, and non-stationary transmission dynamics. This study proposes a novel hybrid probabilistic forecasting framework that integrates Gaussian process regression (GPR) with Holt-Winters exponential smoothing to predict monthly malaria admissions among children under five in Ghana. The approach effectively captures nonlinear patterns while preserving seasonal structure and ensuring long-term stability, and it provides rigorous quantification of predictive uncertainty. The model achieves an R² of 0.9906, with 94.2% of residuals falling within ±2σ, and forecasts monthly admissions between 8,000 and 12,200 cases from 2024 to 2028. These results reveal stable relative patterns amid regional ecological heterogeneity, offering high-precision decision support for national malaria control programs.

Existing probabilistic forecasting evaluation methods lack the ability to characterize tail calibration—critical for high-impact extreme events, whose reliability is increasingly vital for risk-informed decision-making. Method: This paper introduces, for the first time, a general definition of tail calibration, rigorously connecting it to classical probabilistic calibration theory and integrating the Peaks-over-Threshold (POT) framework from extreme value theory. We develop an operational diagnostic framework by unifying probabilistic calibration theory, extreme-value statistics, diagnostic statistical tests, and empirical analysis. Contribution/Results: Applied to European precipitation forecasts, our framework significantly improves the quantification of predictive credibility for high-impact, rare events. It enables rigorous assessment of tail behavior in probabilistic forecasts and establishes a novel paradigm for extreme-event risk assessment and decision support.

This paper addresses the degradation of probabilistic forecast calibration in dynamic data streams caused by distributional shift, feedback loops, and adversarial perturbations. We propose the first general online calibration framework grounded in Blackwell approachability—a theoretically rigorous foundation for sequential decision-making under uncertainty. Our method provides strong calibration guarantees in compact output spaces (e.g., classification and bounded regression) and enables lossless post-hoc recalibration of arbitrary pre-trained predictors. Technically, it unifies insights from Blackwell approachability theory, online optimization, and gradient-based updates, and introduces task-specific efficient algorithms for both classification and regression. Empirical evaluation demonstrates substantial improvements in calibration quality for energy system forecasting, with marked gains in robustness and practical utility for downstream decision-making tasks.

This study addresses a critical limitation in existing probabilistic electricity price forecasting methods, which overly prioritize sharpness at the expense of calibration, yielding overconfident and statistically unreliable uncertainty estimates. The authors systematically analyze the trade-off between calibration and sharpness, demonstrating how prevailing scoring rules—by neglecting reliability—distort predictive distributions and risk degenerating probabilistic models into mere surrogates of deterministic forecasts. To remedy this, the paper proposes a theoretical framework that elevates calibration to a central modeling principle, integrating probabilistic prediction, calibration assessment, and proper scoring rules. It advocates for the development of calibration-aware predictive objectives and architectures, offering a principled direction to enhance the reliability and comprehensiveness of forecasts in energy markets.

This study addresses the uncertainty inherent in seasonal adjustment arising from the unobservability of seasonal components in economic analysis. We propose a probabilistic model discovery method based on Bayesian inference that decomposes time series into seasonal and non-seasonal components, yielding posterior distributions over both structures and parameters. The core innovation lies in establishing the first probabilistic framework to quantify real-time uncertainty in seasonal adjustment, thereby overcoming the limitations of conventional deterministic approaches. Experiments on simulated and macroeconomic datasets demonstrate that the proposed method significantly improves both point and interval forecasting accuracy. Furthermore, it enables the early detection of adjustment risks that traditional tools such as X-13 fail to capture.

This study addresses the limitation of existing recalibration methods, which often obscure miscalibration in specific regions such as extreme events. To overcome this, we propose an outcome-conditional recalibration post-processing method that leverages quantile recalibration and conditional distribution scaling to achieve precise correction of arbitrary predictive distributions within user-defined regions. By simultaneously preserving global performance and local reliability, the proposed approach significantly enhances conditional calibration on regression benchmark tasks. Furthermore, when applied to electricity price forecasting, it substantially improves calibration in negative-price regimes with negligible accuracy loss. Overall, this work provides more reliable localized guarantees for probabilistic forecasting.

This study addresses the persistent challenges of inadequate statistical coverage and inaccurate uncertainty quantification in existing AI-based weather forecasting models, particularly during extreme events. It introduces, for the first time, an online conformal prediction framework that makes no distributional assumptions to post-process outputs from three leading global probabilistic AI models—GenCast, NeuralGCM, and AIFS-ENS. The proposed method significantly improves the statistical coverage accuracy of temperature and precipitation forecasts, including extreme events, without compromising other probabilistic performance metrics. By providing mathematically rigorous uncertainty guarantees, this approach enables reliably calibrated AI-driven weather predictions.

This study addresses the challenge that high penetration of renewable energy exacerbates electricity demand uncertainty, rendering traditional deterministic forecasting inadequate for effective risk quantification. Leveraging real-world power grid data, this work systematically evaluates probabilistic machine learning models, including Natural Gradient Boosting (NGBoost), Bayesian methods, Monte Carlo Dropout, and Gaussian Process Regression. The results demonstrate that NGBoost offers comprehensive advantages in both point forecasting accuracy and uncertainty calibration. It achieves the lowest MAE and RMSE while providing well-calibrated and tight prediction intervals, significantly outperforming baseline models. These findings establish NGBoost as a superior approach, offering more reliable probabilistic decision support for power system planning and operation.