The point of statistical inference is not to produce the right answers with high frequency, but rather to always produce the inferences best supported by the data at hand when combined with existing background knowledge and assumptions. Science is largely not a process of falsifying claims definitively, but rather assigning them probabilities and updating those probabilities in light of observation. This process is endless.
Clayton, A. (2022). Bernoulli’s Fallacy: Statistical illogic and the crisis of modern science. Columbia University Press.
Even more, statistical inference should be understood as a tool to help us efficiently meet the demands of our epistemic duties, especially with regard to questions we want to answer. Ideally, this should be also be sensitive to the contexts in which we are asking, the concrete information we have in hand, and appropriate rational constraints on inference dictated by practical interests for which the inference is conducted.
Insofar as we want to ask, "Which theory is most likely given my data, in my circumstance? Which particular hypothesis is most likely to pay off for me?", we're committed to Probabilism. Insofar as we are interested in holding our probability assignments accountable to empirical data, especially in the sciences and industry, we're committed to Calibration. And insofar as we should be otherwise maximally skeptical about inferences where empirical data is sparse, we're committed to Equivocation. At least on paper, Objective Bayesianism [1] looks pretty good compared to the frequentist status quo as well as compared to subjectivist Bayesian statistical methods. [2]
[1] Williamson, J. (2010). In defence of objective bayesianism. Oxford University Press.
[2] That said, I think the strength of OB is likely in interpretation rather than method, and that there are likely several ways to satisfy OB coming from either the subjective Bayesian methods (injecting Calibration) or from frequentist methods (injecting Probabilism and Equivocation). Such methodological pluralism will likely have several computational boons. But I need to investigate further.
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