Gibbs posterior concentration rates under sub-exponential type losses
| Autor: | Syring, Nicholas, Martin, Ryan |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Bernoulli, volume 29, pages 1080--1108, 2023 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3150/22-BEJ1491 |
| Popis: | Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior computations, plus a potentially serious risk of model misspecification bias. Gibbs posterior distributions, on the other hand, offer direct, principled, probabilistic inference on quantities of interest through a loss function, not a model-based likelihood. Here we provide simple sufficient conditions for establishing Gibbs posterior concentration rates when the loss function is of a sub-exponential type. We apply these general results in a range of practically relevant examples, including mean regression, quantile regression, and sparse high-dimensional classification. We also apply these techniques in an important problem in medical statistics, namely, estimation of a personalized minimum clinically important difference. Comment: 59 pages, 1 figure |
| Databáze: | arXiv |
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