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arxiv: 2510.15096 · v2 · submitted 2025-10-16 · 💻 cs.AI · cs.LG

OpenEstimate: Evaluating LLMs on Reasoning Under Uncertainty with Real-World Data

Alana Renda , Jillian Ross , Michael Cafarella , Jacob Andreas This is my paper

Pith reviewed 2026-05-18 05:50 UTC · model grok-4.3

classification 💻 cs.AI cs.LG
keywords LLM evaluationreasoning under uncertaintyprobabilistic estimationbenchmarkcalibrationoverconfidencenumerical estimation
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The pith

Frontier language models produce inaccurate and overconfident probabilistic priors on real-world numerical estimation tasks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces OpenEstimate, a benchmark of numerical estimation problems drawn from real domains that require models to combine background knowledge into full probability distributions rather than single answers. Evaluation of six frontier models shows their elicited priors deviate from actual data distributions and place excessive probability on wrong outcomes. Changes in elicitation format produce modest gains while sampling strategy, extra reasoning steps, and prompt variations leave performance largely unchanged.

Core claim

The central claim is that LM-elicited priors on OpenEstimate tasks are often inaccurate relative to the true distribution of the quantity being estimated and are overconfident in their probability assignments; performance improves modestly with different uncertainty elicitation methods but shows little sensitivity to sampling strategy, reasoning effort, or prompt design.

What carries the argument

The OpenEstimate benchmark: a set of multi-domain numerical estimation tasks that require synthesis of background information into probabilistic priors, with evaluation against samples from the true distribution.

If this is right

  • LM uncertainty reasoning can be quantified by direct comparison of elicited priors to observed data distributions.
  • Elicitation phrasing affects calibration more than prompt wording or chain-of-thought length.
  • Overconfidence persists across variations in sampling temperature and reasoning budget.
  • The benchmark provides a stable platform for tracking progress on probabilistic estimation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Models might improve if trained explicitly to output calibrated distributions rather than point estimates.
  • The same tasks could reveal whether access to external search or data retrieval reduces overconfidence.
  • Deployment in domains like finance or medicine may need separate uncertainty-handling modules beyond current prompting.

Load-bearing premise

The benchmark problems are ones that humans can answer reliably with correct probabilistic estimates while LMs will struggle without special training.

What would settle it

A frontier model that produces priors closely matching the empirical distribution on most OpenEstimate tasks would falsify the claim of general inaccuracy and overconfidence.

Figures

Figures reproduced from arXiv: 2510.15096 by Alana Renda, Jacob Andreas, Jillian Ross, Michael Cafarella.

Figure 1
Figure 1. Figure 1: Variable generation and prior elicitation pipeline. We construct derived variables from large [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: MAE error ratio of LLM prior to a naive statistical baseline computed using a uninformative [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Expected calibration error (in percentage points) across domains and model families. The best [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Heatmap describing the deviations from perfect calibration of each approach. Bolded [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Cumulative distribution function displaying the percentage of ground truth values that fall [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Relationship between uncertainty and accuracy across domains. Each point shows a model’s [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Effect of elicitation protocol (direct, quantile, mean–variance) on error ratio, expected [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: We examine the impact of changing temperature or reasoning effort on accuracy, calibration, [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: We examine the impact of changing the system prompt or reasoning effort on accuracy, [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
read the original abstract

Real-world settings where language models (LMs) are deployed -- in domains spanning healthcare, finance, and other forms of knowledge work -- require models to grapple with incomplete information and reason under uncertainty. Yet most LM evaluations focus on problems with well-defined answers and success criteria. This gap exists in part because natural problems involving uncertainty are difficult to construct: given that LMs have access to most of the same knowledge as humans, it is non-trivial to design questions for which LMs will struggle to produce correct answers, but which humans can answer reliably. As a result, LM performance on reasoning under uncertainty remains poorly characterized. To address this gap, we introduce OpenEstimate, an extensible, multi-domain benchmark for evaluating LMs on numerical estimation tasks that require models to synthesize significant amounts of background information and express predictions as probabilistic priors. We assess these priors for accuracy and calibration, quantifying their usefulness relative to samples from the true distribution of interest. Across six frontier LMs, we find that LM-elicited priors are often inaccurate and overconfident. Performance improves modestly depending on how uncertainty is elicited from the model, but is largely unaffected by changes in sampling strategy, reasoning effort, or prompt design. The OpenEstimate benchmark thus offers a challenging evaluation for frontier LMs and a platform for developing models that are better at probabilistic estimation and reasoning under uncertainty.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The paper introduces OpenEstimate, an extensible multi-domain benchmark for evaluating LLMs on numerical estimation tasks that require synthesizing background information and expressing predictions as probabilistic priors. Across six frontier LMs, LM-elicited priors are reported to be often inaccurate and overconfident; performance shows modest gains from elicitation method but is largely unaffected by sampling strategy, reasoning effort, or prompt design.

Significance. If the tasks are shown to have objective ground-truth distributions that humans can estimate reliably, the benchmark would address a genuine gap in LM evaluation by focusing on naturalistic uncertainty reasoning rather than well-defined problems. The extensibility and multi-domain coverage are strengths that could support future work on probabilistic estimation.

major comments (1)
  1. [Abstract and §1] Abstract and §1 (Introduction): The motivation explicitly rests on constructing 'natural problems involving uncertainty' for which 'LMs will struggle to produce correct answers, but which humans can answer reliably.' No human performance baselines, expert validation, or inter-rater reliability results are reported on the actual tasks. This is load-bearing for the central claim, because all accuracy and calibration metrics are computed against the authors' chosen ground truths; without evidence that these targets are reliably estimable by humans, poor LM performance could reflect task ambiguity rather than a specific deficit in uncertainty reasoning.
minor comments (3)
  1. [Methods] Methods section: Provide explicit details on task construction, statistical tests for cross-condition comparisons, error bars or confidence intervals on accuracy/calibration metrics, and any data exclusion rules. These are needed to evaluate the robustness of the claim that performance is largely unaffected by sampling strategy, reasoning effort, or prompt design.
  2. [Results] Results: Consider including per-model tables or figures with confidence intervals to support the reported modest effects from elicitation method.
  3. [Appendix] Reproducibility: Include all task prompts, examples, and ground-truth sources in an appendix or supplementary material.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed review and for identifying a key aspect of our motivation. We address the major comment below and outline targeted revisions to the manuscript.

read point-by-point responses

  1. Referee: [Abstract and §1] Abstract and §1 (Introduction): The motivation explicitly rests on constructing 'natural problems involving uncertainty' for which 'LMs will struggle to produce correct answers, but which humans can answer reliably.' No human performance baselines, expert validation, or inter-rater reliability results are reported on the actual tasks. This is load-bearing for the central claim, because all accuracy and calibration metrics are computed against the authors' chosen ground truths; without evidence that these targets are reliably estimable by humans, poor LM performance could reflect task ambiguity rather than a specific deficit in uncertainty reasoning.

    Authors: We agree that explicit human performance baselines would strengthen the central motivation. The ground-truth distributions, however, are not subjective estimates but are derived directly from objective, publicly verifiable real-world data sources (government statistics, published reports, and empirical studies). The tasks require synthesizing background information that is generally accessible, and the evaluation measures LM deviation from these fixed targets rather than from human judgments. We will revise §1 and the abstract to more explicitly state the objective, data-driven nature of the ground truths and add a dedicated paragraph in the limitations section acknowledging the lack of human baselines while outlining plans for such validation in follow-up work. This addresses the concern without requiring new experiments in the current revision. revision: partial

Circularity Check

0 steps flagged

No circularity in empirical benchmark evaluation

full rationale

This paper presents an empirical benchmark (OpenEstimate) for assessing LLMs on numerical estimation and uncertainty reasoning tasks drawn from real-world domains. It contains no derivations, equations, fitted parameters renamed as predictions, or first-principles results. Claims rest on direct experimental measurements of accuracy and calibration against author-chosen ground-truth distributions, with no self-definitional loops, load-bearing self-citations, or ansatzes smuggled via prior work. The methodology is self-contained as a standard evaluation study; performance differences are reported as observed outcomes rather than constructed equivalences. No steps reduce the central findings to inputs by definition.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The evaluation rests on the domain assumption that suitable tasks exist where humans can answer reliably while frontier models cannot, plus standard benchmarking assumptions about ground-truth availability for accuracy and calibration scoring.

axioms (1)
  • domain assumption Natural problems involving uncertainty can be designed such that LMs struggle to produce correct answers but humans can answer reliably
    Explicitly stated in the abstract as the reason the evaluation gap exists and the benchmark is needed.

pith-pipeline@v0.9.0 · 5777 in / 1274 out tokens · 34830 ms · 2026-05-18T05:50:21.219799+00:00 · methodology

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Reference graph

Works this paper leans on

47 extracted references · 47 canonical work pages

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    **Consider the context**: Reflect on what {{variable}} represents and any relevant information you have about its population-level average

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    **Construct the prior**: Express the distribution in the form: $$ \mu\sim\mathcal{N}(\mu_0, \sigma_0ˆ2) $$ where$\mu_0$is your belief about the central tendency and$\sigma_0$ reflects the degree of confidence (epistemic uncertainty) in that belief

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    --- ### Important Guidance * Do **not** base$\sigma_0$on the variability **across individuals** in the population

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    Consider the context of the variable, including its meaning and any relevant information that informs your beliefs

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    Estimate the following percentiles of the parameter’s true value: - 5th percentile (only a 5% chance the true value is below this) - 25th percentile - 50th percentile (median - your best estimate of the true value) - 75th percentile - 95th percentile (only a 5% chance the true value is above this)

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    Explicitly state the type of parameter being estimated (e.g., population mean, proportion)

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    Estimate the following quantities: - Best guess: your estimate of the most likely value of the population-level parameter (e.g., mean or proportion) - Standard deviation or variance: a numerical expression of your uncertainty about the true value not the variability across individual observations

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    Include the following elements: - Clearly state the type of parameter being estimated (e.g., population mean, true proportion)

    Begin your analysis by showing your thought process inside <parameter_estimation_process> tags. Include the following elements: - Clearly state the type of parameter being estimated (e.g., population mean, true proportion). - List any known facts, data points, or previous estimates about the variable. - Consider possible data sources, analogous population...

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    After your analysis, provide your final answer in the following format: <mean>[Best guess for the true value]</mean> <std_dev>[Standard deviation representing your uncertainty]</std_dev> <justification> [Brief summary of your reasoning and what informed your estimates] </justification> <confidence_level> [Explanation of how confident or uncertain you are,...

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    The standard deviation reflects uncertainty due to potential sampling biases and regional variations

    Gaussian (Normal) Distribution Example: Variable: Average height of adult males in a country Units: Centimeters <mean>175</mean> <std_dev>2.5</std_dev> <justification> Based on global averages, previous studies in similar populations, and considering factors like nutrition and genetics. The standard deviation reflects uncertainty due to potential sampling...

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    The standard deviation accounts for potential biases in available data and variations across different demographics

    Beta Distribution Example: Variable: Proportion of people who prefer tea over coffee in a city Units: Proportion (0 to 1) <mean>0.6</mean> <std_dev>0.05</std_dev> <justification> Estimated based on local cultural preferences, limited survey data, and comparison with similar cities. The standard deviation accounts for potential biases in available data and...

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