Deep Fiducial Inference

Generalized fiducial inference(GFI) Hannig et al.(2016), a modern reincarnation of R. A. Fisher's fiducial inference(Fisher, 1930), provides inferentially meaningful probability statements about subsets of parameter space without the need for subjective prior information. GFI specifies a generalized fiducial distribution (GFD) by defining a data-dependent measure on the parameter space through an inverse of a data-generating algorithm (see Sections 2). Data-generating algorithm plays the role of a model and is sometimes called data-generating equation or data-generating function. With GFD as a distribution estimator for the fixed parameter, we can further define approximate confidence (fiducial) sets which are often shown in simulation to have very desired properties. Given the data-generating algorithm and the corresponding density of the GFD, one could form point estimate and asymptotic confidence sets similarly as with a Bayesian posterior density. Standard MCMC-type sampling techniques have already been successfully implemented in many situations; see Hannig et al. (2016) and the references therein.