From Stochasticity to Signal: A Bayesian Latent State Model for Reliable Measurement with LLMs

Large Language Models (LLMs) are increasingly used to automate classification tasks in business, such as analyzing customer satisfaction from text. However, the inherent stochasticity of LLMs, in terms of their tendency to produce different outputs for the same input, creates a significant measurement error problem that is often neglected with a single round of output, or addressed with ad-hoc methods like majority voting. Such naive approaches fail to quantify uncertainty and can produce biased estimates of population-level metrics. In this paper, we propose a principled solution by reframing LLM variability as a statistical measurement error problem and introducing a Bayesian latent state model to address it. Our model treats the true classification (e.g., customer dissatisfaction) as an unobserved latent variable and the multiple LLM ratings as noisy measurements of this state. This framework allows for the simultaneous estimation of the LLM's false positive and false negative error rates, the underlying base rate of the phenomenon in the population, the posterior probability of the true state for each individual observation, and the causal impact of a business intervention, if any, on the latent state. Through simulation studies, we demonstrate that our model accurately recovers true parameters where naive methods fail. We conclude that this methodology provides a general and reliable framework for converting noisy, probabilistic outputs from LLMs into accurate and actionable insights for scientific and business applications.