Probabilistic Forecasting

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Probabilistic forecasting estimates ranges, quantiles, event probabilities, or full predictive distributions rather than only a single future value. Methods include Bayesian and parametric models, ensemble post-processing and conformal calibration, and neural generative approaches such as diffusion and flow matching; language-model agents also forecast real-world events using evidence and probability aggregation. Researchers evaluate forecasts with proper scores such as CRPS and Brier score, alongside calibration, sharpness, and benchmarks in weather, energy, health, finance, and human mobility. A central challenge is balancing accuracy, reliable uncertainty, computational cost, and usefulness for downstream decisions, since strong average scores may hide failures in extremes or dependencies between outcomes.

Latest papers

230 papers37 papers in the last four weeks, up 3% on the four weeks before. 0.2% of all new papers.

Verifiable Rewards for Calibrated Probabilistic Forecasting
Jun 30, 2026Sadanand Singh, Allam Reddy, Manan ChopraProbability Calibration RL for Language Model Reasoning
Cascade Research
Measuring Judgment Quality in Natural-Language Explanations: Evidence from Forecasting Tournaments
Jun 29, 2026Christopher W. Karvetski, Sheldon S. Huang, Simas Kučinskas +4LLM-as-a-Judge Probabilistic Forecasting
Forecasting Research Institute · Good Judgment Inc · University of Toronto +4
Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias
Jun 29, 2026Yujin Kim, Nidhi Soma, Sarah DeanProbabilistic Forecasting Uncertainty Calibration
Department of Computer Science Cornell University Ithaca, NY, 14853
EO-WM: A Physically Informed World Model for Probabilistic Earth Observation Forecasting
Jun 25, 2026Junwei Luo, Shuai Yuan, Zhenya Yang +3World Model Learning Forecasting Benchmarks
1The University of Hong Kong · 2Wuhan University
Rethinking Training & Inference for Forecasting: Linking Winner-Take-All back to GMMs
Jun 24, 2026Qiyuan Wu, Katie Z Luo, Bharath Hariharan +2Gaussian Mixture Models Probabilistic Forecasting
Cornell University · Stanford University · Boston University
Otter Weather: Skillful and Computationally Efficient Medium-Range Weather Forecasting
Jun 24, 2026Cristiana Diaconu, Jonas Scholz, Aliaksandra Shysheya +4Time Series Forecasting Probabilistic Forecasting
University of Cambridge
Sampling sea state using a diffusion model
Jun 24, 2026Jiarong Wu, Bertrand Chapron, Laure ZannaTime Series Forecasting Probabilistic Forecasting
Courant Institute School of Mathematics, Computing and Data Science, New York University, 251 Mercer Street, New York, 10012, NY, USA. · Laboratoire d’Oc´eanographie Physique et Spatiale (LOPS), Ifremer, 1625 route de Sainte-Anne, Plouzan´e, 29280, Bretagne, France.
Gaussian Mean Field Variational Inference can Overestimate Predictive Variance
Jun 24, 2026James Odgers, Ben Riegler, Siddharth Swaroop +1Probabilistic Forecasting Variational Inference
University of Technology Nuremberg (UTN) · Helmholtz AI · Munich Center for Machine Learning (MCML) +2
Model selection with proper scoring rules on data sets of time series: prefer the mean scaled score
Jun 23, 2026Giorgio Corani, Stefano Damato, Dario Azzimonti +1Model Selection Time Series Forecasting
SUPSI, Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA), Lugano, Switzerland
Distribution-Aware Diffusion-LLM for Robust Ultra-Long-Term Time Series Forecasting
Jun 22, 2026Falguni Ghosh, Vahid Hashemi, Bernhard KainzLong-Term Time Series Forecasting Probabilistic Forecasting
Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, 91052, Germany · AUDI AG, Auto-Union-Straße 1, 85057 Ingolstadt, Germany · Imperial College London, London SW7 2RH, United Kingdom
Beyond Time Series: Spatial Reasoning for Epidemic Forecasting via Multimodal Learning
Jun 20, 2026Diana Guadalupe Gomez, Chenwei Wu, Zhiyi Wang +2Epidemic Forecasting Spatiotemporal Reasoning
University of Michigan Ann Arbor, MI, USA
VegSim: A Geospatial World Model for Scenario-Conditioned Vegetation Simulation
Jun 20, 2026Irene Iele, Elena Mulero Ayllón, Paolo Soda +1World Models Probabilistic Forecasting
Università Campus Bio-Medico di Roma Rome, Italy · Umeå University Umeå, Sweden · University of Genoa Genoa, Italy
Continuous-Time Probabilistic Correctors for Uncertainty-Aware Physics-Based Spacecraft Trajectory Forecasting
Jun 19, 2026Muhammad Bilal Shahid, Zhanhong Jiang, Soumik Sarkar +1Neural Controlled Differential Equations Uncertainty Quantification
Iowa State University, Ames, Iowa, 50011, USA
Online Distributional Prediction via Latent Cluster Geometry Under Drift and Corruption
Jun 17, 2026Navyansh Mahla, Prateek Chanda, Ganesh RamakrishnanDistribution Shift Robustness Probabilistic Forecasting
Indian Institute of Technology, Bombay
ForecastBench-Sim: A Simulated-World Forecasting Benchmark
Jun 17, 2026Jaeho Lee, Nick Merrill, Ezra KargerForecasting Benchmarks Probabilistic Forecasting
1Forecasting Research Institute · 2UC Berkeley
Toward Simultaneously Optimal Regret in U-Calibration
Jun 16, 2026Rafael Frongillo, Haipeng Luo, Nishant A. Mehta +1Follow-the-Perturbed-Leader Probabilistic Forecasting
University of Colorado Boulder · University of Southern California and Google Research · University of Victoria +1
Pointwise is Pointless? A Multimodal Ablation Study for Precipitation Nowcasting with Graph Neural Networks
Jun 16, 2026Ophélia Miralles, Máté Mile, Christoffer Artturi +2Precipitation Forecasting Probabilistic Forecasting
Norwegian Meteorological Institute, Oslo, Norway
Reinforcement Learning for LLM-based Event Forecasting
Jun 14, 2026Amit Arnold LevyEvent Time Prediction RL for Language Models
University of Oxford
Navigating the Safety-Fidelity Trade-off: Massive-Variate Time Series Forecasting for Power Systems via Probabilistic Scenarios
Jun 11, 2026Kaijie Xu, Anqi Wang, Xilin DaiMultivariate Time Series Forecasting Forecasting Benchmarks
ZJU-UIUC Institute Zhejiang University Hangzhou, China
Reliability of Probabilistic Emulation of Physical Systems
Jun 11, 2026Sam F. Greenbury, Radka Jersakova, Paolo Conti +4Surrogate Modeling Probabilistic Forecasting
The Alan Turing Institute · Autodesk Research · PhysicsX +3
WorldReasoner: Evaluating Whether Language Model Agents Forecast Events with Valid Reasoning
Jun 10, 2026Yizhou Chi, Eric Chamoun, Zifeng Ding +1Event Time Prediction LLM Agent Evaluation
Department of Computer Science and Technology University of Cambridge
First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systems
Jun 9, 2026Shreya Jha, Timo Schorlepp, Nicholas Geissler +2Dynamical Systems Surrogate Modeling
Courant Institute of Mathematical Sciences, New York University
Investigating Calibration Challenges in Probabilistic Electricity Price Forecasting
Jun 8, 2026Jan Niklas Lettner, Hadeer El Ashhab, Benjamin SchäferProbability Calibration Electricity Price Forecasting
Institute for Automation and Applied Informatics
Improving the sharpness in neural network-based parametric post-processing of ensemble forecasts
Jun 7, 2026Ágnes Baran, Máté MihalinaProbabilistic Forecasting Regression Prediction Intervals
Faculty of Informatics, University of Debrecen, Debrecen, Hungary
Proper Scoring Rules for Right-Censored Survival Data
Jun 4, 2026Jef Jonkers, Glenn Van Wallendael, Luc Duchateau +1Survival Analysis Probabilistic Forecasting
IDLab Department of Electronics and Information Systems Ghent University, Belgium · IDLab Department of Electronics and Information Systems Ghent University - imec, Belgium · Biometrics Research Group Department of Morphology, Imaging, Orthopedics, Rehabilitation and Nutrition Ghent University, Belgium
Function-Space Priors for Bayesian Neural ODEs with Application to Vessel Trajectory Prediction
Jun 4, 2026Jaeyeong Lee, Wonmo Koo, Heeyoung KimBayesian Neural Networks Probabilistic Forecasting
aDepartment of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea.
ReSGA: A Large Tail Risk Model for Learning Value-at-Risk and Expected Shortfall
Jun 3, 2026Yichi Zhang, Ke Zhu, Zhoufan ZhuQuantitative Finance Autoencoders
Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong · Wang Yanan Institute for Studies in Economics, Xiamen University, China · Department of Finance, School of Economics, Xiamen University, China
DiffUNet^2: Bidirectional Conditional Diffusion for Probabilistic Scientific Spatiotemporal Modeling
Jun 2, 2026Mengdi Chu, Jiaxin Yang, Angus G. Forbes +4Diffusion Model Guidance Probabilistic Forecasting
Mengdi Chu, Jiaxin Yang, and Han-Wei Shen are with the Ohio State University. · Angus G. Forbes is with NVIDIA. · Nathan Debardeleben, Earl Lawrence, Ayan Biswas are with Los Alamos National Laboratory.
AdaWeather: Adaptively Mixing Probabilistic Weather Forecasts with Logarithmic Regret
Jun 1, 2026Saptarishi Dhanuka, Sarvesh Iyer, Manmeet Singh +5Probabilistic Forecasting Mixture-of-Experts Models
Ashoka University · Ashoka University, India · Western Kentucky University
Bayesian Inference of Nonlinear Malaria Dynamics in Ghana via an Ensemble Markov Chain Monte Carlo Sampler
May 30, 2026T. Ansah-Narh, Y. Asare Afrane, J. Bremang TandohEpidemic Forecasting Bayesian Inference
Ghana Space Science and Technology Institute, Ghana Atomic Energy Commission, P. O. Box LG 80, Legon, Accra, Ghana · Department of Medical Microbiology, University of Ghana Medical School, University of Ghana, Accra, Ghana

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Verifiable Rewards for Calibrated Probabilistic Forecasting

Sadanand Singh, Allam Reddy, Manan Chopra

Cascade Research

Probability Calibration RL for Language Model Reasoning Probabilistic Forecasting Reinforcement Learning with Verifiable Rewards Sports Outcome Prediction Reward Design for RL

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Reinforcement learning with verifiable rewards can in principle train calibrated probabilistic forecasters, since a proper scoring rule such as the Brier score is computed from outcomes alone and is minimized in expectation by the true probability. In practice it degrades calibration, and existing remedies address epistemic uncertainty, where a model's confidence accompanies a verifiably correct or incorrect answer. We study aleatoric forecasting, where the forecast itself is the output and the label is one stochastic outcome, taking NFL in-game win probability as a testbed with the betting market as a reference. Rewarding the realized per-play outcome fails, because the single outcome is a noisy target and the policy gradient corrupts the chain of thought. We introduce a verifiable, label-free reward, a state-conditioned empirical win rate estimated from past outcomes, that removes the label noise, and we keep the gradient off the reasoning, by direct prediction or a gradient mask, so it cannot be corrupted. Trained with this reward alone, without human labels or supervised fine-tuning, a 7B model reaches the calibration of the betting market by direct prediction and is better calibrated than a zero-shot frontier model. That frontier model and a tabular estimator reach the same Brier score as this model, identifying the market's small remaining edge as live in-game information beyond their shared inputs. Masking the gradient, rather than dropping the chain of thought, preserves reasoning from which the forecast follows, which ordinary chain-of-thought training corrupts.