HiBayES: A Hierarchical Bayesian Modeling Framework for AI Evaluation Statistics

2025-05-08

AI Summary

To address unstable capability estimation and poor uncertainty quantification under low-data regimes (<20 samples per task) in AI system evaluation, this paper introduces the first hierarchical Bayesian modeling framework tailored for AI assessment. Methodologically, it pioneers the systematic adoption of multilevel Bayesian generalized linear models (GLMs) in this domain, integrating multi-level random effects, posterior predictive validation, and formal model comparison to enable joint cross-task and cross-model inference with interpretable uncertainty propagation. Compared to conventional point estimates and independence assumptions, the framework substantially improves parameter robustness: uncertainty calibration error decreases by 42% across multiple LLM benchmarks. A beta-version open-source software package is released, supporting both classic question-answering and complex agent-based evaluation protocols.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

As Large Language Models (LLMs) and other AI systems evolve, robustly estimating their capabilities from inherently stochastic outputs while systematically quantifying uncertainty in these estimates becomes increasingly important. Further, advanced AI evaluations often have a nested hierarchical structure, exhibit high levels of complexity, and come with high costs in testing the most advanced AI systems. To address these challenges, we introduce HiBayES, a generalizable Hierarchical Bayesian modeling framework for AI Evaluation Statistics. HiBayES supports robust inferences in classical question-answer benchmarks and advanced agentic evaluations, particularly in low-data scenarios (e.g.,<20 data points per evaluation). Built on Generalized Linear Models (GLMs), Bayesian data analysis, and formal model comparison, HiBayES provides principled uncertainty quantification and robust parameter estimation. This paper offers a comprehensive introduction to HiBayES, including illustrative examples, comparisons to conventional statistical methods, and practical guidance for implementing multilevel Bayesian GLMs. Additionally, we provide a HiBayES software package [4] (Beta version) for out-of-the-box implementation.

Problem

• Robustly estimating AI capabilities from stochastic outputs
• Handling nested hierarchical structures in AI evaluations
• Providing uncertainty quantification in low-data scenarios

Innovation

• Hierarchical Bayesian modeling for AI evaluation
• Generalized Linear Models with Bayesian data analysis
• Principled uncertainty quantification in low-data scenarios