This chapter motivates why, and under which circumstances, the explanatory power of a scientific hypothesis with respect to a body of evidence can be explicated by means of statistical relevance. This account is traced back to its historic roots in Peirce and Hempel and defended against its critics (e.g., contrasting statistical relevance to purely causal accounts of explanation). Then we derive various Bayesian explications of explanatory power using the method of representation theorems and we compare their properties from a normative point of view. Finally we evaluate how such measures of explanatory power can ground a theory of Inference to the Best Explanation (IBE).
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