Matching prior pairs connecting Maximum A Posteriori estimation and posterior expectation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910625849933824 |
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| author | Okudo, Michiko Yano, Keisuke |
| author_facet | Okudo, Michiko Yano, Keisuke |
| contents | Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We derive an asymptotic condition for a pair of prior densities under which the posterior mean based on one prior coincides with the MAP estimate based on the other prior. A sufficient condition for the existence of this prior pair relates to $α$-flatness of the statistical model in information geometry. We also construct a matching prior pair using $α$-parallel priors. Our result elucidates an interesting connection between regularization in generalized linear regression models and posterior expectation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09586 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Matching prior pairs connecting Maximum A Posteriori estimation and posterior expectation Okudo, Michiko Yano, Keisuke Statistics Theory Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We derive an asymptotic condition for a pair of prior densities under which the posterior mean based on one prior coincides with the MAP estimate based on the other prior. A sufficient condition for the existence of this prior pair relates to $α$-flatness of the statistical model in information geometry. We also construct a matching prior pair using $α$-parallel priors. Our result elucidates an interesting connection between regularization in generalized linear regression models and posterior expectation. |
| title | Matching prior pairs connecting Maximum A Posteriori estimation and posterior expectation |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2312.09586 |