BayesBench: Evaluating LLM Belief Trajectories Under Multi-Turn Evidence Accumulation
06:00 · July 1, 2026 · arXiv cs.AI RSS
Large language models (LLMs) are typically deployed in multi-turn conversations, where each turn provides new evidence that should reduce epistemic uncertainty about their environment. Acting rationally then requires inferring the unobserved quantities that govern it and updating beliefs about them as evidence accumulates. Yet most evaluations only score the model's final-turn answer in a single-turn format, leaving this process unexamined. We ask how closely LLMs' belief updates match those of a rational Bayesian reasoner in multi-turn settings, and introduce BayesBench, a suite of simulation environments that probe this across three progressively complex tasks: (i) Bayesian estimation, where the model infers an unknown parameter from sequential evidence; (ii) Bayesian prediction, where the model turns inferred beliefs about a latent variable into outcome forecasts; and (iii) latent-framed Bayesian prediction, where observations are filtered through a user-persona framing, requiring joint inference over the latent state and the persona. Across seven LLMs (3B--70B), scaling improves latent inference and evidence accumulation, with updates occasionally matching the Bayesian posterior. However, these gains do not reliably carry over to downstream prediction, exposing a gap between inferring latent structure and using it to rationally update beliefs about the target outcome.
Summary
Large language models are routinely placed in multi-turn dialogues in which successive messages supply new observations that should, in principle, reduce uncertainty about hidden aspects of the environment. Rational behavior in such settings requires the model to infer the latent quantities that govern the observations and to revise its beliefs accordingly as evidence arrives. Existing benchmarks, however, typically evaluate only the final answer in a single-turn format, leaving the intermediate belief-updating process unexamined.
BayesBench addresses this gap with a family of simulation environments that compare model behavior against an ideal Bayesian reasoner across three tasks of increasing complexity. In the first, Bayesian estimation, the model must recover an unknown parameter from a sequence of noisy observations. In the second, Bayesian prediction, the inferred posterior over the latent variable is used to forecast future outcomes. The third task, latent-framed Bayesian prediction, introduces an additional layer: observations are presented through a user-persona framing, forcing the model to perform joint inference over both the latent state and the persona that shapes how evidence is reported.
Experiments with seven models ranging from 3 B to 70 B parameters show that larger scale improves the ability to accumulate evidence and to approximate the true Bayesian posterior over the latent variable. These improvements, however, do not translate consistently into more accurate downstream predictions. The resulting dissociation indicates that current models can sometimes track latent structure without reliably converting that structure into coherent updates about the quantities they are ultimately asked to forecast.
Why it matters
This research provides a rigorous framework for evaluating the reasoning and reliability of LLMs in dynamic, multi-turn environments. For Dutch AI researchers and developers, understanding and benchmarking these epistemic updates is crucial for building trustworthy, transparent AI systems that align with EU standards.
