Using large language models to suggest informative prior distributions in Bayesian regression analysis
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View abstract on PubMed
Summary
This summary is machine-generated.Large language models (LLMs) can suggest informative prior distributions for Bayesian regression, aiding objective analysis. While capable of identifying correct associations, calibrating prior distribution width remains a challenge for LLMs.
Area Of Science
- Bayesian statistics
- Machine learning
- Statistical modeling
Background
- Selecting prior distributions in Bayesian regression is complex and subjective.
- Existing methods for eliciting informative priors are resource-intensive and difficult to perform objectively.
Purpose Of The Study
- To investigate the potential of large language models (LLMs) in suggesting suitable prior distributions for Bayesian regression analysis.
- To evaluate the performance of different LLMs in generating knowledge-based and objective informative priors.
Main Methods
- Developed an extensive prompt for LLMs to suggest, verify, and reflect on prior distributions.
- Evaluated three LLMs (Claude Opus, Gemini 2.5 pro, ChatGPT 4o-mini) on two real-world datasets (heart disease risk, concrete strength).
- Assessed prior distribution quality using Kullback-Leibler divergence against the maximum likelihood estimator's distribution.
Main Results
- LLMs successfully suggested the correct direction of associations for variables in both datasets.
- Claude and Gemini generally outperformed ChatGPT in suggesting prior distributions.
- Moderate informative priors suggested by LLMs were often too confident, showing limited agreement with the data.
- Claude demonstrated an advantage by not defaulting to a mean of 0 for weakly informative priors, unlike ChatGPT and Gemini.
Conclusions
- LLMs show significant potential for developing efficient and objective informative prior distributions in Bayesian regression.
- A key challenge lies in calibrating the width of LLM-suggested priors, as they exhibit tendencies towards overconfidence and underconfidence.
- Claude Opus exhibited a notable advantage in its approach to suggesting priors compared to Gemini and ChatGPT.
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