Generalized fiducial inference

Abstract

Generalized Fiducial Inference provides a recipe for constructing confidence intervals as well as tools for establishing the asymptotically correct coverage of many of these intervals. Confidence intervals based on the generalized fiducial framework have been applied to a wide range of problems, many of which lack exact pivots, and these intervals have exhibited excellent asymptotic and small sample performance. Generalized fiducial inference has also been used for model selection and simultaneous inference. In this article, the generalized fiducial framework is presented along with important results and applications. In the process, simple examples are used to illustrate the intuition behind and the application of the framework and its tools. WIREs Comput Stat 2014, 6:132–143. doi: 10.1002/wics.1291 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

What type of Type I error? Contrasting the Neyman–Pearson and Fisherian approaches in the context of exact and direct replications

“…At one point, fiducial inference was described as being "essentially dead" (Pedersen, 1978, p. 147). Contrary to this view, there has been a renewed interest in fiducial inference, with several statisticians currently investigating various instantiations of this idea (e.g., Bowater, 2017;Hampel, 2003;Heike et al, 2007;Iverson, 2014;Veronese & Melilli, 2015; for reviews, see Hannig, Iyer, Lai, & Lee, 2016;Rønneberg, 2017). It is beyond the scope of the current paper (and the competency of its author) to consider the fiducial argument in detail.…”

Confidence Distribution and Distribution Estimation for Modern Statistical Inference

“…We briefly overview these modern approaches which extend Fisher's original fiducial argument. We then focus on a recent development termed generalized fiducial inference and its applications (Hannig, 2009;Cisewski and Hannig, 2012;Wandler and Hannig, 2012;Iverson, 2014;Lai et al, 2015b;Hannig et al, 2016;Hannig, 2016, 2017;Cui and Hannig, 2019a;Neupert and Hannig, 2019) that greatly expand the applicability of fiducial ideas. We demonstrate this recipe on several examples of varying complexity.…”