The Problem of the Priors, or Posteriors?
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913918521180160 |
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| author | Lin, Hanti |
| author_facet | Lin, Hanti |
| contents | The problem of the priors is well known: it concerns the challenge of identifying norms that govern one's prior credences. I argue that a key to addressing this problem lies in considering what I call the problem of the posteriors -- the challenge of identifying norms that directly govern one's posterior credences, which backward induce some norms on the priors via the diachronic requirement of conditionalization. This forward-looking approach can be summarized as: Think ahead, work backward. Although this idea can be traced to Freedman (1963), Carnap (1963), and Shimony (1970), I believe that it has not received enough attention. In this paper, I initiate a systematic defense of forward-looking Bayesianism, addressing potential objections from more traditional views (both subjectivist and objectivist). I also develop a specific approach to forward-looking Bayesianism -- one that values the convergence of posterior credences to the truth, and treats it as a fundamental rather than derived norm. This approach, called convergentist Bayesianism, is argued to be crucial for a Bayesian foundation of Ockham's razor in statistics and machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Problem of the Priors, or Posteriors? Lin, Hanti Other Statistics Artificial Intelligence Probability The problem of the priors is well known: it concerns the challenge of identifying norms that govern one's prior credences. I argue that a key to addressing this problem lies in considering what I call the problem of the posteriors -- the challenge of identifying norms that directly govern one's posterior credences, which backward induce some norms on the priors via the diachronic requirement of conditionalization. This forward-looking approach can be summarized as: Think ahead, work backward. Although this idea can be traced to Freedman (1963), Carnap (1963), and Shimony (1970), I believe that it has not received enough attention. In this paper, I initiate a systematic defense of forward-looking Bayesianism, addressing potential objections from more traditional views (both subjectivist and objectivist). I also develop a specific approach to forward-looking Bayesianism -- one that values the convergence of posterior credences to the truth, and treats it as a fundamental rather than derived norm. This approach, called convergentist Bayesianism, is argued to be crucial for a Bayesian foundation of Ockham's razor in statistics and machine learning. |
| title | The Problem of the Priors, or Posteriors? |
| topic | Other Statistics Artificial Intelligence Probability |
| url | https://arxiv.org/abs/2503.10984 |