Statistics

   

Data-Driven Priors Via Hyper-Parameter Posteriors of Gaussian Processes

Authors: L. Martino, J. Lopez-Santiago, J. Miguez, G. Vazquez-Vilar

When neither prior knowledge nor expert opinion is available, non-informative priors provide a practical alternative for conducting Bayesian inference. However, in the context of model selection, genuinely non-informative priors do not exist. In fact, diu2000use priors on the parameters can drastically alter the value of the Bayesian evidence, making them effectively highly informative, while improper priors are even not allowed. Furthermore, in many real-worldapplications, the use of informative priors can substantially improve the computational efficiency by driving sampling algorithms toward regions of high posterior probability. In this work, we introduce a data-driven procedure for an automatic prior construction. The underlying idea is to exploit the posteriors of the hyper-parameters from non-parametric models, to construct priors for Bayesian inference in parametric models. We test the proposed scheme in four different experiments, two of which involve real astronomical data.

Comments: 26 Pages.

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[v1] 2025-10-04 10:00:17

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