# AI4BayesCode: From Natural Language Descriptions to Validated Modular Stateful Bayesian Samplers

arXiv: https://arxiv.org/abs/2605.18476 · HTML: https://mlsanity.com/paper/2605.18476/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 44 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 19 of 19)

- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Agentic Harness Engineering: Observability-Driven Automatic Evolution of Coding-Agent Harnesses](https://mlsanity.com/paper/2604.25850/) (2026)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [Externalization in LLM Agents: A Unified Review of Memory, Skills, Protocols and Harness Engineering](https://mlsanity.com/paper/2604.08224/) (2026)
- [Natural-Language Agent Harnesses](https://mlsanity.com/paper/2603.25723/) (2026)
- [Hamiltonian Monte Carlo for Hierarchical Models](https://mlsanity.com/paper/1312.0906/) (2013)
- [LLM-Based Test-Driven Interactive Code Generation: User Study and Empirical Evaluation](https://mlsanity.com/paper/2404.10100/) (2024)
- [Pareto Smoothed Importance Sampling](https://mlsanity.com/paper/1507.02646/) (2015)
- [Bayesian Regression Tree Ensembles that Adapt to Smoothness and Sparsity](https://mlsanity.com/paper/1707.09461/) (2017)
- [LAMBDA: A Large Model Based Data Agent](https://mlsanity.com/paper/2407.17535/) (2024)
- [AI Agentic Programming: A Survey of Techniques, Challenges, and Opportunities](https://mlsanity.com/paper/2508.11126/) (2025)
- [A Survey of Vibe Coding with Large Language Models](https://mlsanity.com/paper/2510.12399/) (2025)
- [Bayesian Concept Bottleneck Models with LLM Priors](https://mlsanity.com/paper/2410.15555/) (2024)
- [AutoElicit: Using Large Language Models for Expert Prior Elicitation in Predictive Modelling](https://mlsanity.com/paper/2411.17284/) (2024)
- [Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacy](https://mlsanity.com/paper/2202.09924/) (2022)
- [A Comprehensive Survey of AI-Driven Advancements and Techniques in Automated Program Repair and Code Generation](https://mlsanity.com/paper/2411.07586/) (2024)
- [LLM-Prior: A Framework for Knowledge-Driven Prior Elicitation and Aggregation](https://mlsanity.com/paper/2508.03766/) (2025)
- [LLM-BI: Towards Fully Automated Bayesian Inference with Large Language Models](https://mlsanity.com/paper/2508.08300/) (2025)
- [AutoStan: Autonomous Bayesian Model Improvement via Predictive Feedback](https://mlsanity.com/paper/2603.27766/) (2026)

## Abstract (arXiv)

Coding and computation remain major bottlenecks in Markov chain Monte Carlo (MCMC) workflows, especially as modern sampling algorithms have become increasingly complex and existing probabilistic programming systems remain limited in model support, extensibility, and composability. We introduce AI4BayesCode, an extensible LLM-driven system that translates natural-language Bayesian model descriptions into runnable, validated MCMC samplers. To improve reliability, AI4BayesCode adopts a modular design that decomposes models into modular sampling blocks and maps each block to a built-in sampling component, reducing the need to implement complex sampling algorithms from scratch. Reliability is further improved through pre-generation validation of model specifications and post-generation validation of generated sampler code. AI4BayesCode also introduces a novel recursively stateful coding paradigm for MCMC, allowing modular sampling components, potentially developed by different contributors, to be composed coherently within larger MCMC procedures. We develop a benchmark suite to evaluate AI4BayesCode for sampler-generation. Experiments show that AI4BayesCode can implement a wide range of Bayesian models from natural-language descriptions alone. As an open-ended system, its capability can continue to expand with improvements in the underlying AI agent and the addition of new built-in blocks. The software is available at https://ai4bayescode.com/.