A new look at fiducial inference
By: Pier Giovanni Bissiri, Chris Holmes, Stephen Walker
Potential Business Impact:
Makes statistics more reliable for predictions.
Since the idea of fiducial inference was put forward by Fisher, researchers have been attempting to place it within a rigorous and well motivated framework. It is fair to say that a general definition has remained elusive. In this paper we start with a representation of Bayesian posterior distributions provided by Doob that relies on martingales. This is explicit in defining how a true parameter value should depend on a random sample and hence an approach to "inverse probability" as originally conceived by Fisher. Taking this as our cue, we introduce a definition of fiducial inference that can be regarded as general.
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