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

Abstract: 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.