Foundation Priors

Sanjog Misra

Papers from arXiv.org

Abstract: Foundation models, and in particular large language models, can generate highly informative responses, prompting growing interest in using these ''synthetic'' outputs as data in empirical research and decision-making. This paper introduces the idea of a foundation prior, which shows that model-generated outputs are not as real observations, but draws from the foundation prior induced prior predictive distribution. As such synthetic data reflects both the model's learned patterns and the user's subjective priors, expectations, and biases. We model the subjectivity of the generative process by making explicit the dependence of synthetic outputs on the user's anticipated data distribution, the prompt-engineering process, and the trust placed in the foundation model. We derive the foundation prior as an exponential-tilted, generalized Bayesian update of the user's primitive prior, where a trust parameter governs the weight assigned to synthetic data. We then show how synthetic data and the associated foundation prior can be incorporated into standard statistical and econometric workflows, and discuss their use in applications such as refining complex models, informing latent constructs, guiding experimental design, and augmenting random-coefficient and partially linear specifications. By treating generative outputs as structured, explicitly subjective priors rather than as empirical observations, the framework offers a principled way to harness foundation models in empirical work while avoiding the conflation of synthetic ''facts'' with real data.

Date: 2025-11
New Economics Papers: this item is included in nep-ain and nep-mac
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2512.01107 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2512.01107

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().