Agentic Forecasting using Sequential Bayesian Updating of Linguistic Beliefs

Probabilistic forecasting estimates the likelihood of uncertain future events. To improve LLM forecasting, existing methods typically learn from binary outcomes to output verbalized forecasts. However, while aggregated human forecasts contain rich information in both the crowd probability estimate and the degree of agreement among forecasters, how to utilize these signals remains underexplored. To address this, we propose the Beta-Bernoulli Calibrator (BBC), which converts an initial point estimate forecast from any model into a distribution over event likelihood, using supervision from both binary outcomes and human forecasts. BBC models event likelihood $p \sim \text{Beta}(α, β)$ and outcome $y \sim \text{Bernoulli}(p)$, with the mean as the calibrated point forecast and the variance as the epistemic uncertainty. Our results show that BBC generally provides better calibrated and more accurate forecasts than both traditional post-hoc calibration methods and models fine-tuned specifically for forecasting, while remaining lightweight and having good generalization. We also show that the epistemic uncertainty captured by BBC is a more reliable predictor of forecasting error than verbalized confidence.

LLM-based forecasting systems have improved on real-world tasks such as financial markets and sports outcomes, largely through stronger search and tool use. Many systems still ask an LLM to read all collected evidence together and produce the final forecast. We call this design Monolithic Prediction. It can obscure how individual evidence items affect the result and collapse uncertainty across competing outcomes. We propose LEAP (Likelihood Elicitation and Aggregation for Probabilistic forecasting), which reorganizes how collected evidence is used in the prediction stage. LEAP examines each evidence item separately and elicits likelihood parameters that describe its implications for the target. An explicit prior and a deterministic probabilistic model then combine these likelihoods into a posterior distribution. This procedure supports continuous, single-choice, and multi-choice forecasts while preserving reproducible evidence contributions. We build a benchmark covering forecasting, information-seeking, and browsing tasks, and evaluate LEAP on our own agent loop and several agent CLI frameworks. Given the same evidence, LEAP improves most prediction and calibration metrics across models and remains stronger under controlled comparisons of prior access, inference budget, and aggregation.

In hybrid forecasting, a language model is often one of several available signals. A system may already have a market, crowd, or statistical forecast and must decide whether the model adds useful information or should be ignored. The relevant target is therefore not standalone model accuracy, but relative competence, defined as the model's marginal value beyond the available external forecast. Under Brier loss, we characterize when model disagreement can improve an external forecast and derive the gain from using domain-specific rather than global pooling weights. We then introduce a competence gate that estimates domain-level source weights from resolved outcomes, shrinks uncertain estimates toward a global weight, and recalibrates the pooled forecast. Across 2,357 resolved binary questions and five language models, the gate improves the main external baseline from 0.0771 to 0.0732 Brier and significantly outperforms global forecast combinations. The gain remains significant under leakage controls and against a leakage-safe time-series prior on the pooled structured set, with separate evidence on FRED. In contrast, the gate gives no significant improvement on the official ForecastBench market subset, where it largely defers to the market. Across four Qwen models, verbal confidence does not reliably identify when the model outperforms the external forecast, while outcome-estimated competence supports better abstention decisions. These results provide a practical approach for selective model use based on measured marginal value.