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Abstract:
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Severity (Mayo, 2018) is the degree of warrant accorded to an inferential claim resulting from an inferential strategy in relation to a body of evidence. Extending the Popperian notion of falsifiability, severity seeks to establish a stochastic version of modus tollens, as a measure of strength of probabilistic inference. If the available evidence leads a strategy to infer something about the world, then were it not the case, would the strategy still have inferred it?
I discuss the formulation of warrant and severity in general statistical inference tasks of both the frequentist and Bayesian traditions. I investigate the properties of the warrant function, including coherence and informativeness, and demonstrate its assessment and interpretation with examples. A connection with significance function (Fraser, 1991) and confidence distribution (Xie & Singh, 2013) is drawn. This vocabulary may enable the assessment of warrant and severity in a wide range of modern applications that call for evidence-based scientific decision making.
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