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BayesJudge: Uncertainty-Aware Bayesian Meta-Evaluation of Human and LLM Judgments

NeurIPS 2026 · Large language models › Language, safety and interpretability · approach: Statistical frameworks for LLM evaluation

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Proposes BayesJudge, an online Bayesian meta-evaluation layer that infers panel-relative posterior verdicts over {A, Tie, B} while jointly estimating human rater confusion matrices and LLM position bias via paired AB/BA swaps, using a Rao-Blackwellized assumed-density SMC filter.

Problem

Pairwise AI evaluation yields conflicting human and LLM judgments; majority vote or single LLM queries collapse ambiguity, and LLM position bias and human rater noise are modeled separately if at all.

Approach

Jointly models a latent ternary verdict (A/Tie/B) per item with Dawid-Skene-style human confusion matrices and a scalar LLM position-bias term, using tie-open labels and order-swapped judge calls as identification instruments, with streaming SMC inference.

Key results

• On SummEval leave-one-human-out, BayesJudge reaches 65.3% expert accuracy versus 46.3% for Bradley-Terry-Davidson and 38.0% for MACE, and ECE 0.042 on crowdworkers.
• Synthetic confusion-matrix recovery reduces Frobenius error from 0.332 to 0.065 (expert) and 1.136 to 0.054 (novice).
• Posterior entropy correlates with human voting entropy on SummEval (Spearman rho=0.404, p<10^-40).

Surprising findings

• On crowdworker prediction, BayesJudge (42.3% accuracy) underperforms the human-only channel (68.9%) and MACE (69.1%), trading crowd accuracy for expert accuracy.
• Forced-choice-only data cannot identify tie mass, so tie-open labels are required for ambiguity estimation.

Limitations

• Only scalar LLM position bias is modeled; other biases such as length are not handled in the experiments.
• Few human annotations per item and inconsistent annotators across items constrain bias modeling on SummEval.
• The implemented MAP-profile and hard-MAP Dirichlet updates are approximations; the exact posterior target is not what is run.

Experimental setup

Datasets: SummEval synthetic pairwise comparison dataset

Benchmarks: SummEval synthetic pairwise stream

Metrics: accuracy NLL Brier score ECE Frobenius error held-out predictive log likelihood Spearman correlation

Baselines: Majority-Vote Bradley-Terry-Davidson MACE GLAD

Builds on: Dawid-Skene Bradley-Terry-Davidson MACE GLAD

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