  The origins of fiducial inference trace back to the 1930s when R. A. Fisher
first introduced the concept as a response to what he perceived as a limitation
of Bayesian inference - the requirement for a subjective prior distribution on
model parameters in cases where no prior information was available. However,
Fisher's initial fiducial approach fell out of favor as complications arose,
particularly in multi-parameter problems. In the wake of 2000, amidst a renewed
interest in contemporary adaptations of fiducial inference, generalized
fiducial inference (GFI) emerged to extend Fisher's fiducial argument,
providing a promising avenue for addressing numerous crucial and practical
inference challenges. Nevertheless, the adoption of GFI has been limited due to
its often demanding mathematical derivations and the necessity for implementing
complex Markov Chain Monte Carlo algorithms. This complexity has impeded its
widespread utilization and practical applicability. This paper presents a
significant advancement by introducing an innovative variant of GFI designed to
alleviate these challenges. Specifically, this paper proposes AutoGFI, an
easily implementable algorithm that streamlines the application of GFI to a
broad spectrum of inference problems involving additive noise. AutoGFI can be
readily implemented as long as a fitting routine is available, making it
accessible to a broader audience of researchers and practitioners. To
demonstrate its effectiveness, AutoGFI is applied to three contemporary and
challenging problems: tensor regression, matrix completion, and regression with
network cohesion. These case studies highlight the immense potential of GFI and
illustrate AutoGFI's promising performance when compared to specialized
solutions for these problems. Overall, this research paves the way for a more
accessible and powerful application of GFI in a range of practical domains.
