---
title: "LLMs Are Not (Consistently) Bayesian: Quantifying Internal (In)consistencies of LLMs’ Probabilistic Beliefs"
description: "LLMs are deployed in medicine, science, and law, where observed evidence may not determine a single correct answer and systems must represent and update uncertain beliefs. The work treats LLMs as information processing rules and measures an information processing gap, defined as deviation from Bayes updates, to quantify internal consistency in probabilistic belief updates. Extensive experiments compare multiple ways of incorporating evidence: some yield nearly Bayesian updates, while others rely on learned heuristics. Although exact Bayesian updating is optimal information processing, the non-Bayesian heuristic updates often achieve better downstream task performance, suggesting that the LLMs’ probabilistic models of the world are misspecified. The measure also serves as a diagnostic for issues in LLM-powered inferential systems."
---

# LLMs Are Not (Consistently) Bayesian: Quantifying Internal (In)consistencies of LLMs’ Probabilistic Beliefs

[Apple](https://yomu.fyi/company/apple) · Aug 28, 2026

**Type:** Explainer

## Summary

LLMs are deployed in medicine, science, and law, where observed evidence may not determine a single correct answer and systems must represent and update uncertain beliefs. The work treats LLMs as information processing rules and measures an information processing gap, defined as deviation from Bayes updates, to quantify internal consistency in probabilistic belief updates. Extensive experiments compare multiple ways of incorporating evidence: some yield nearly Bayesian updates, while others rely on learned heuristics. Although exact Bayesian updating is optimal information processing, the non-Bayesian heuristic updates often achieve better downstream task performance, suggesting that the LLMs’ probabilistic models of the world are misspecified. The measure also serves as a diagnostic for issues in LLM-powered inferential systems.

## Context

Modern AI systems are being deployed in medicine, science, and law, where there is often not a single correct answer given the observed evidence. They need to represent and update uncertain beliefs as new evidence arrives in order to make rational decisions.

## Approach / What changed

The work studies LLMs as information processing rules and uses the information processing gap—the deviation from Bayes updates—to measure how they update probabilistic beliefs from evidence. Experiments evaluate multiple evidence-incorporation approaches, including exact Bayesian updates and learned heuristics, and apply the measure to diagnose issues in LLM-powered inferential systems.

## Takeaways

- The information processing gap quantifies how an LLM’s belief update deviates from a Bayes update.
- Some evidence-incorporation approaches produce nearly Bayesian updates, while others use learned heuristics.
- Non-Bayesian heuristic updates often outperform exact Bayesian updates on downstream tasks, indicating misspecified probabilistic models of the world.

**Tags:** [LLMs](https://yomu.fyi/topic/llm), [Machine Learning](https://yomu.fyi/topic/machine-learning), [Performance](https://yomu.fyi/topic/performance), [Reliability](https://yomu.fyi/topic/reliability)

- Source: [Apple](https://machinelearning.apple.com/research/llms-not-consistently-bayesian)
- Source URL: https://machinelearning.apple.com/research/llms-not-consistently-bayesian
- Ingested by Yomu: 2026-08-28T16:00:48.195Z

[Read original post](https://machinelearning.apple.com/research/llms-not-consistently-bayesian)