How to Run Statistics over LLM Judges and Trust the Results: Calibrated Inference for Small-Sample AI Evaluation with evalstats

arXiv:2609.35815 · cs.CL, cs.AI, cs.HC, stat.ME · Submitted 2026-09-20 · Read on arXiv

cs.CL, cs.AI, cs.HC, stat.ME

Submitted: 2026-09-20

Updated: 2026-09-20

Code: https://github.com/ianarawjo/evalstats

Project page: https://statsforevals.com

Terminology

• LLM judge — 111× in this paper · explained in 2 episodes
• Alignment — 48× in this paper · explained in 1 episode
• Benchmark — 36× in this paper · explained in 2 episodes
• Calibration — 24× in this paper · explained in 7 episodes
• Pairwise Comparisons — 9× in this paper · explained in 2 episodes
• LLM-as-a-Judge — 7× in this paper · explained in 3 episodes
• Benchmarking — 5× in this paper · explained in 3 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Synthetic Data Generation — 4× in this paper · explained in 5 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Consistency — 3× in this paper · explained in 3 episodes
• Robustness — 3× in this paper · explained in 5 episodes
• Uncertainty Quantification — 3× in this paper · explained in 8 episodes
• Deep Reinforcement Learning — 2× in this paper · explained in 2 episodes
• Exchangeability — 2× in this paper · explained in 2 episodes
• Influence Functions — 2× in this paper · explained in 2 episodes
• Reinforcement Learning — 2× in this paper · explained in 4 episodes
• Sycophancy — 2× in this paper · explained in 4 episodes
• Systematic Bias — 2× in this paper · explained in 3 episodes
• AUC — 1× in this paper · explained in 2 episodes
• Ablation — 1× in this paper · explained in 1 episode
• Accountability — 1× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Adversarial scenarios — 1× in this paper · explained in 1 episode
• Aggregation — 1× in this paper · explained in 1 episode
• Bayesian Framework — 1× in this paper · explained in 3 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Data Provenance — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Nadia — 1× in this paper · explained in 2 episodes
• National Institute for Standards and Technology — 1× in this paper
• Non-asymptotic Analysis — 1× in this paper · explained in 2 episodes
• Post-Selection — 1× in this paper · explained in 2 episodes
• Prompt Engineering — 1× in this paper · explained in 4 episodes
• Provenance — 1× in this paper · explained in 4 episodes
• RAG — 1× in this paper · explained in 3 episodes
• Semi-supervised Learning — 1× in this paper · explained in 4 episodes
• Steering — 1× in this paper · explained in 2 episodes
• alpha — 1× in this paper · explained in 1 episode

Sources

• PPI++: Efficient Prediction-Powered Inference
• Guidelines for Empirical Studies in Software Engineering involving Large Language Models
• Power Analysis for Prediction-Powered Inference
• Bias and Uncertainty in LLM-as-a-Judge Estimation
• Which Metrics Save the Most Human Annotation? Prediction-Powered Evaluation and Meta-Evaluation
• Do Repetitions Matter? Strengthening Reliability in LLM Evaluations
• This human study did not involve human subjects: Validating LLM simulations as behavioral evidence
• Adding Error Bars to Evals: A Statistical Approach to Language Model Evaluations
• Programming by Chat: A Large-Scale Behavioral Analysis of 11,579 Real-World AI-Assisted IDE Sessions
• Generalized Prediction-Powered Inference, with Application to Binary Classifier Evaluation
• A Note on the Prediction-Powered Bootstrap

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