The General Formulation of Loss-Based Priors for Parameter Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908983050108928 |
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| author | Villa, Cristiano |
| author_facet | Villa, Cristiano |
| contents | Loss-based priors assign probability mass to parameter values according to the inferential loss incurred when they are excluded from the parameter space, and provide a general solution for discrete parameters. Extending this idea to continuous settings is challenging, as the exclusion of a single point induces no loss. We propose a neighbourhood-exclusion framework in which inferential loss is defined by removing a local region around each parameter value. Under standard regularity conditions, this yields a class of prior distributions driven by the local geometry of the Kullback--Leibler divergence. In one dimension, the resulting prior coincides with Jeffreys' prior, while in higher dimensions it leads to a family of priors indexed by the geometry of the exclusion region. The proposed formulation provides a unified extension of loss-based priors and offers a geometric interpretation of objective prior construction beyond isotropic settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19150 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The General Formulation of Loss-Based Priors for Parameter Spaces Villa, Cristiano Methodology Statistics Theory Loss-based priors assign probability mass to parameter values according to the inferential loss incurred when they are excluded from the parameter space, and provide a general solution for discrete parameters. Extending this idea to continuous settings is challenging, as the exclusion of a single point induces no loss. We propose a neighbourhood-exclusion framework in which inferential loss is defined by removing a local region around each parameter value. Under standard regularity conditions, this yields a class of prior distributions driven by the local geometry of the Kullback--Leibler divergence. In one dimension, the resulting prior coincides with Jeffreys' prior, while in higher dimensions it leads to a family of priors indexed by the geometry of the exclusion region. The proposed formulation provides a unified extension of loss-based priors and offers a geometric interpretation of objective prior construction beyond isotropic settings. |
| title | The General Formulation of Loss-Based Priors for Parameter Spaces |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2604.19150 |