The Problem of the Priors, or Posteriors?

Abstract: 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.