AgentBayes: Open-Ended Scientific Model Discovery

Scientific data modeling often requires more than predicting observations; it must recover the probabilistic data-generating structure: how observations are nested, how variation arises at each level, and how uncertainty propagates through to predictions. We introduce AgentBayes, an agentic system for Bayesian model discovery on real scientific datasets. AgentBayes automates the iterative Bayesian workflow through two roles: an Interactor that explores raw data and fitted posteriors through executable analysis, and a Modeler that converts these findings into hierarchical probabilistic programs. Because data and posterior samples remain in an executable sandbox rather than being serialized into LLM context, AgentBayes can critique and revise models at dataset scales where prior agentic Bayesian systems exhaust the context window. Across five posteriordb benchmarks and three scientific case studies, AgentBayes matches or improves on expert-written Bayesian models on most datasets, scales to larger datasets than prior agentic Bayesian systems, and outperforms symbolic regression baselines on data with experimental hierarchy. AgentBayes also surfaces overlooked data structure in existing benchmarks, and adapts its probabilistic programs accordingly. Together, these results show that LLM agents can aid scientists by performing the full Bayesian workflow, from exploratory data analysis to open-ended posterior predictive checks, on real-world, large-scale scientific data, broadening LLM-based scientific discovery from equation search to full probabilistic modeling.