A Bayesian perspective on severity: risky predictions and specific hypotheses.

ABSTRACT

A tradition that goes back to Sir Karl R. Popper assesses the value of a statistical test primarily by its severity was there an honest and stringent attempt to prove the tested hypothesis wrong? For "error statisticians" such as Mayo (1996, 2018), and frequentists more generally, severity is a key virtue in hypothesis tests. Conversely, failure to incorporate severity into statistical inference, as allegedly happens in Bayesian inference, counts as a major methodological shortcoming. Our paper pursues a double goal First, we argue that the error-statistical explication of severity has substantive drawbacks; specifically, the neglect of research context and the specificity of the predictions of the hypothesis. Second, we argue that severity matters for Bayesian inference via the value of specific, risky predictions severity boosts the expected evidential value of a Bayesian hypothesis test. We illustrate severity-based reasoning in Bayesian statistics by means of a practical example and discuss its advantages and potential drawbacks.