Regularized e-processes: anytime valid inference with knowledge-based efficiency gains
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913089714126848 |
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| author | Martin, Ryan |
| author_facet | Martin, Ryan |
| contents | Classical statistical methods have theoretical justification when the sample size is predetermined. In applications, however, it's often the case that sample sizes are data-dependent rather than predetermined. The aforementioned methods aren't reliable in this latter case, hence the recent interest in e-processes and methods that are anytime valid, i.e., reliable for any dynamic data-collection plan. But if the investigator has relevant-yet-incomplete prior information about the quantity of interest, then there's an opportunity for efficiency gain. This paper proposes a regularized e-process framework featuring a knowledge-based, imprecise-probabilistic regularization with improved efficiency. A generalized version of Ville's inequality is established, ensuring that inference based on the regularized e-process are anytime valid in a novel, knowledge-dependent sense. Regularized e-processes also facilitate possibility-theoretic uncertainty quantification with strong frequentist-like calibration properties and other Bayesian-like properties: satisfies the likelihood principle, avoids sure-loss, and offers formal decision-making with reliability guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01427 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularized e-processes: anytime valid inference with knowledge-based efficiency gains Martin, Ryan Statistics Theory Probability Methodology Classical statistical methods have theoretical justification when the sample size is predetermined. In applications, however, it's often the case that sample sizes are data-dependent rather than predetermined. The aforementioned methods aren't reliable in this latter case, hence the recent interest in e-processes and methods that are anytime valid, i.e., reliable for any dynamic data-collection plan. But if the investigator has relevant-yet-incomplete prior information about the quantity of interest, then there's an opportunity for efficiency gain. This paper proposes a regularized e-process framework featuring a knowledge-based, imprecise-probabilistic regularization with improved efficiency. A generalized version of Ville's inequality is established, ensuring that inference based on the regularized e-process are anytime valid in a novel, knowledge-dependent sense. Regularized e-processes also facilitate possibility-theoretic uncertainty quantification with strong frequentist-like calibration properties and other Bayesian-like properties: satisfies the likelihood principle, avoids sure-loss, and offers formal decision-making with reliability guarantees. |
| title | Regularized e-processes: anytime valid inference with knowledge-based efficiency gains |
| topic | Statistics Theory Probability Methodology |
| url | https://arxiv.org/abs/2410.01427 |