Generalized Fiducial Inference: A Review and New Results
By Jan Hannig, Hari Iyer, Randy C. S. Lai, Thomas C.M. Lee. 2016
234 citations recorded by the source corpus.
Abstract R. A. Fisher, the father of modern statistics, proposed the idea of fiducial inference during the first half of the 20th century. While his proposal led to interesting methods for quantifying uncertainty, other prominent statisticians of the time did not accept Fisher’s approach as it became apparent that some of Fisher’s bold claims about the properties of fiducial distribution did not hold up for multi-parameter problems. Beginning around the year 2000, the authors and collaborators started to reinvestigate the idea of fiducial inference and discovered that Fisher’s approach, when properly generalized, would open doors to solve many important and difficult inference problems. They termed their generalization of Fisher’s idea as generalized fiducial inference (GFI). The main idea of GFI is to carefully transfer randomness from the data to the parameter space using an inverse of a data-generating equation without the use of Bayes’ theorem. The resulting generalized fiducial distribution (GFD) can then be used for inference. After more than a decade of investigations, the authors and collaborators have developed a unifying theory for GFI, and provided GFI solutions to many challenging practical problems in different fields of science and industry. Overall, they have demonstrated that GFI is a valid, useful, and promising approach for conducting statistical inference. The goal of this article is to deliver a timely and concise introduction to GFI, to present some of the latest results, as well as to list some related open research problems. It is authors’ hope that their contributions to GFI will stimulate the growth and usage of this exciting approach for statistical inference. Supplementary materials for this article are available online.
Subfields: Statistical and Nonlinear Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/2fec01882785ed71860151302c03e9f73003e17b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Statistical and Nonlinear Physics
In Statistics and Probability
- Cynthia Rudin
- Gary King
- Ryan Martin
- Yili Hong
- Beau Coker
- Nicholas Syring
- Peter C. Austin
- Debasis Kundu
Citations in the corpus
- Applications of the Fractional-Random-Weight Bootstrap (2018, background): “• Generalized fiducial inference (GFI), which is also known as generalized pivotal quantity (see Hannig, Iyer, and Patterson 2006, Majumder and Hannig 2016, and Hannig et al. 2016), has proven to be a powerful tool for defining confidence interval procedures for non-standard models.”
- An imprecise-probabilistic characterization of frequentist statistical inference (2021, background): “2006), fiducial (Fisher 1935, 1973a), generalized fiducial (Hannig et al. 2016), structural (Fraser 1968), or confidence distributions (Schweder and Hjort 2016; Xie and Singh 2013).”
- A Theory of Statistical Inference for Ensuring the Robustness of Scientific Results (2018, methodology): “Head et al. (2015) concluded that the evidence indicates the existence of “widespread” evidence for p-hacking after searching all Open Access papers in the PubMed database (∼ 100, 000 papers).”
- Calibrating general posterior credible regions (2015, background): “It also covers classical empirical Bayes or other posteriors based on data-dependent priors (e.g., Fraser et al. 2010; Hannig et al. 2016; Martin and Walker 2016).”