AutoGFI: Streamlined Generalized Fiducial Inference for Modern Inference Problems in Models with Additive Errors

The concept of fiducial inference was introduced by R. A. Fisher in the 1930s to address the perceived limitations of Bayesian inference, particularly the need for subjective prior distributions in cases with limited prior information. However, Fisher's fiducial approach lost favor due to complications, especially in multi-parameter problems. With renewed interest in fiducial inference in the 2000s, generalized fiducial inference (GFI) emerged as a promising extension of Fisher's ideas, offering new solutions for complex inference challenges. Despite its potential, GFI's adoption has been hindered by demanding mathematical derivations and complex implementation requirements, such as Markov Chain Monte Carlo (MCMC) algorithms. This paper introduces AutoGFI, a streamlined variant of GFI designed to simplify its application across various inference problems with additive noise. AutoGFI's accessibility lies in its simplicity-requiring only a fitting routine-making it a feasible option for a wider range of researchers and practitioners. To demonstrate its efficacy, AutoGFI is applied to three challenging problems: tensor regression, matrix completion, and network cohesion regression. These case studies showcase AutoGFI's competitive performance against specialized solutions, highlighting its potential to broaden the application of GFI in practical domains, ultimately enriching the statistical inference toolkit.