HiBayES: A Hierarchical Bayesian Modeling Framework for AI Evaluation Statistics

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.