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

arXiv: https://arxiv.org/abs/2604.01896 · HTML: https://mlsanity.com/paper/2604.01896/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 2 Apr 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 8 of 8)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [Conformal Prediction with Large Language Models for Multi-Choice Question Answering](https://mlsanity.com/paper/2305.18404/) (2023)
- [API Is Enough: Conformal Prediction for Large Language Models Without Logit-Access](https://mlsanity.com/paper/2403.01216/) (2024)
- [Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens](https://mlsanity.com/paper/2508.01191/) (2025)
- [Large Language Models are overconfident and amplify human bias](https://mlsanity.com/paper/2505.02151/) (2025)
- [Overconfidence in LLM-as-a-Judge: Diagnosis and Confidence-Driven Solution](https://mlsanity.com/paper/2508.06225/) (2025)

## Built on by (most cited first, 1 of 1)

- [CausalDS: Benchmarking Causal Reasoning in Data-Science Agents](https://mlsanity.com/paper/2607.08093/) (2026)

## Abstract (arXiv)

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.