Epistemic Confidence Statement via Extended Likelihood

Abstract

Fisher's fiducial probability has recently attracted renewed attention under the notion of epistemic confidence. Epistemic confidence statements can be formulated through extended likelihoods, thereby clarifying several long-standing controversies regarding its fiducial probability properties. It establishes a direct connection between Fisher's epistemic notion of confidence for observed data and Neyman's frequentist aleatory coverage probability for future data, thereby enabling extension of epistemic confidence statements for multidimensional parameters. We demonstrate how higher-order asymptotic theory can be applied to refine the first-order asymptotic epistemic confidence statements of the observed region, as a direct consequence of extended likelihood property.