A possibility-theoretic solution to Basu's Bayesian--frequentist via media
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915374663991296 |
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| author | Martin, Ryan |
| author_facet | Martin, Ryan |
| contents | Basu's via media is what he referred to as the middle road between the Bayesian and frequentist poles. He seemed skeptical that a suitable via media could be found, but I disagree. My basic claim is that the likelihood alone can't reliably support probabilistic inference, and I justify this by considering a technical trap that Basu stepped in concerning interpretation of the likelihood. While reliable probabilistic inference is out of reach, it turns out that reliable possibilistic inference is not. I lay out my proposed possibility-theoretic solution to Basu's via media and I investigate how the flexibility afforded by my imprecise-probabilistic solution can be leveraged to achieve the likelihood principle (or something close to it). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17425 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A possibility-theoretic solution to Basu's Bayesian--frequentist via media Martin, Ryan Statistics Theory Methodology Other Statistics Basu's via media is what he referred to as the middle road between the Bayesian and frequentist poles. He seemed skeptical that a suitable via media could be found, but I disagree. My basic claim is that the likelihood alone can't reliably support probabilistic inference, and I justify this by considering a technical trap that Basu stepped in concerning interpretation of the likelihood. While reliable probabilistic inference is out of reach, it turns out that reliable possibilistic inference is not. I lay out my proposed possibility-theoretic solution to Basu's via media and I investigate how the flexibility afforded by my imprecise-probabilistic solution can be leveraged to achieve the likelihood principle (or something close to it). |
| title | A possibility-theoretic solution to Basu's Bayesian--frequentist via media |
| topic | Statistics Theory Methodology Other Statistics |
| url | https://arxiv.org/abs/2303.17425 |