The Problem of the Priors, or Posteriors?
This addresses foundational issues in Bayesian epistemology and statistics, potentially influencing norms in machine learning, but it is incremental as it builds on prior philosophical work.
The paper tackles the problem of priors in Bayesianism by proposing a forward-looking approach that focuses on norms for posterior credences, which backward induce priors via conditionalization, and develops convergentist Bayesianism to value convergence to truth as a fundamental norm.
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.