# Confidence in Large Language Model Evaluation: A Bayesian Approach to Limited-Sample Challenges

arXiv: https://arxiv.org/abs/2504.21303 · HTML: https://mlsanity.com/paper/2504.21303/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 44 references that are in the map.
- First posted on arXiv 30 Apr 2025.

## Builds on (most cited first, 28 of 28)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [Adding Error Bars to Evals: A Statistical Approach to Language Model Evaluations](https://mlsanity.com/paper/2411.00640/) (2024)
- [Investigating Data Contamination in Modern Benchmarks for Large Language Models](https://mlsanity.com/paper/2311.09783/) (2023)
- [LaMini-LM: A Diverse Herd of Distilled Models from Large-Scale Instructions](https://mlsanity.com/paper/2304.14402/) (2023)
- [KOR-Bench: Benchmarking Language Models on Knowledge-Orthogonal Reasoning Tasks](https://mlsanity.com/paper/2410.06526/) (2024)
- [SuperCLUE: A Comprehensive Chinese Large Language Model Benchmark](https://mlsanity.com/paper/2307.15020/) (2023)
- [Data Contamination Quiz: A Tool to Detect and Estimate Contamination in Large Language Models](https://mlsanity.com/paper/2311.06233/) (2023)
- [Benchmarking Knowledge Boundary for Large Language Models: A Different Perspective on Model Evaluation](https://mlsanity.com/paper/2402.11493/) (2024)
- [A Survey on Data Contamination for Large Language Models](https://mlsanity.com/paper/2502.14425/) (2025)
- [Reliable and Efficient Amortized Model-based Evaluation](https://mlsanity.com/paper/2503.13335/) (2025)
- [Towards Reproducible LLM Evaluation: Quantifying Uncertainty in LLM Benchmark Scores](https://mlsanity.com/paper/2410.03492/) (2024)
- [ProcBench: Benchmark for Multi-Step Reasoning and Following Procedure](https://mlsanity.com/paper/2410.03117/) (2024)
- [Statistical Knowledge Assessment for Large Language Models](https://mlsanity.com/paper/2305.10519/) (2023)

## Built on by (most cited first, 8 of 8)

- [Don't Pass@k: A Bayesian Framework for Large Language Model Evaluation](https://mlsanity.com/paper/2510.04265/) (2025)
- [Do Repetitions Matter? Strengthening Reliability in LLM Evaluations](https://mlsanity.com/paper/2509.24086/) (2025)
- [Autonomous Agents for Scientific Discovery: Orchestrating Scientists, Language, Code, and Physics](https://mlsanity.com/paper/2510.09901/) (2025)
- [EBPO: Empirical Bayes Shrinkage for Stabilizing Group-Relative Policy Optimization](https://mlsanity.com/paper/2602.05165/) (2026)
- [Sequential Bayesian Evaluation of Large Language Model Behavior](https://mlsanity.com/paper/2511.10661/) (2025)
- [STEM: Efficient Relative Capability Evaluation of LLMs through Structured Transition Samples](https://mlsanity.com/paper/2508.12096/) (2025)
- [Correcting Prompt Dependence in LLM Benchmarks: A Bayesian Hierarchical Model with Embedding-Space Clustering](https://mlsanity.com/paper/2510.05709/) (2025)
- [Are Benchmarks Reliable? Toward Structural Diagnosis via Item-Level Capability Boundaries](https://mlsanity.com/paper/2609.33196/) (2026)

## Abstract (arXiv)

Large language models (LLMs) exhibit probabilistic output characteristics, yet conventional evaluation frameworks rely on deterministic scalar metrics. This study introduces a Bayesian approach for LLM capability assessment that integrates prior knowledge through probabilistic inference, addressing limitations under limited-sample regimes. By treating model capabilities as latent variables and leveraging a curated query set to induce discriminative responses, we formalize model ranking as a Bayesian hypothesis testing problem over mutually exclusive capability intervals. Experimental evaluations with GPT-series models demonstrate that the proposed method achieves superior discrimination compared to conventional evaluation methods. Results indicate that even with reduced sample sizes, the approach maintains statistical robustness while providing actionable insights, such as probabilistic statements about a model's likelihood of surpassing specific baselines. This work advances LLM evaluation methodologies by bridging Bayesian inference with practical constraints in real-world deployment scenarios.