# Large Language Bayes

arXiv: https://arxiv.org/abs/2504.14025 · HTML: https://mlsanity.com/paper/2504.14025/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2025.

## Built on by (most cited first, 10 of 10)

- [Modeling Open-World Cognition as On-Demand Synthesis of Probabilistic Models](https://mlsanity.com/paper/2507.12547/) (2025)
- [A Probabilistic Framework for LLM-Based Model Discovery](https://mlsanity.com/paper/2602.18266/) (2026)
- [Language-Informed Synthesis of Rational Agent Models for Grounded Theory-of-Mind Reasoning On-The-Fly](https://mlsanity.com/paper/2506.16755/) (2025)
- [Likelihood Hacking in Probabilistic Program Synthesis](https://mlsanity.com/paper/2603.24126/) (2026)
- [AdaptFuse: Training-Free Sequential Preference Inference via Externalized Bayesian Computation](https://mlsanity.com/paper/2604.03925/) (2026)
- [AutoStan: Autonomous Bayesian Model Improvement via Predictive Feedback](https://mlsanity.com/paper/2603.27766/) (2026)
- [Probabilistic Programs of Thought](https://mlsanity.com/paper/2604.17290/) (2026)
- [Structured Inference with Large Language Gibbs](https://mlsanity.com/paper/2606.19264/) (2026)
- [Program Synthesis for Simulation-Based Inference: Joint Model Selection and Parameter Estimation](https://mlsanity.com/paper/2607.17540/) (2026)
- [Large Language Bayes Is Not Reparameterisation-Invariant](https://mlsanity.com/paper/2610.00265/) (2026)

## Abstract (arXiv)

Many domain experts do not have the time or expertise to write formal Bayesian models. This paper takes an informal problem description as input, and combines a large language model and a probabilistic programming language to define a joint distribution over formal models, latent variables, and data. A posterior over latent variables follows by conditioning on observed data and integrating over formal models. This presents a challenging inference problem. We suggest an inference recipe that amounts to generating many formal models from the large language model, performing approximate inference on each, and then doing a weighted average. This is justified and analyzed as a combination of self-normalized importance sampling, MCMC, and importance-weighted variational inference. Experimentally, this produces sensible predictions from only data and an informal problem description, without the need to specify a formal model.