Bayesian Elicitation with LLMs: Model Size Helps, Extra "Reasoning" Doesn't Always

TL;DR

This study evaluates large language models' ability to perform Bayesian elicitation, revealing that larger models are more accurate but overconfident, and that additional reasoning effort does not consistently improve estimates.

Contribution

The paper demonstrates that larger LLMs produce better estimates, overconfidence is prevalent, and conformal prediction effectively calibrates their uncertainty intervals.

Findings

Larger models yield more accurate estimates.

Models are severely overconfident with low coverage.

Conformal prediction corrects overconfidence, achieving desired coverage.

Abstract

Large language models (LLMs) have been proposed as alternatives to human experts for estimating unknown quantities with associated uncertainty, a process known as Bayesian elicitation. We test this by asking eleven LLMs to estimate population statistics, such as health prevalence rates, personality trait distributions, and labor market figures, and to express their uncertainty as 95\% credible intervals. We vary each model's reasoning effort (low, medium, high) to test whether more "thinking" improves results. Our findings reveal three key results. First, larger, more capable models produce more accurate estimates, but increasing reasoning effort provides no consistent benefit. Second, all models are severely overconfident: their 95\% intervals contain the true value only 9--44\% of the time, far below the expected 95\%. Third, a statistical recalibration technique called conformal prediction can correct this overconfidence, expanding the intervals to achieve the intended coverage. In a preliminary experiment, giving models web search access degraded predictions for already-accurate models, while modestly improving predictions for weaker ones. Models performed well on commonly discussed topics but struggled with specialized health data. These results indicate that LLM uncertainty estimates require statistical correction before they can be used in decision-making.