Fiducial Distributions in Fiducial Inference

Fiducial Inference for Discrete Distributions: Binomial and Poisson Cases

Generalized Fiducial Inference: A Review

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...

Generalized Fiducial Inference via Discretization

Abstract: In addition to the usual sources of error that have been long studied by statisticians, many data sets have been rounded off in some manner, either by the measuring device or storage on a computer. In this paper we investigate theoretical properties of generalized fiducial distribution introduced in Hannig (2009) for discretized data. Limit theorems are provided for both fixed sample ...

Fiducial Inference and Belief Functions

One aspect of Fisher’s work which has puzzled a great many statisticians is the idea of Fiducial Inference. Using “pivotal” variables, Fisher moves from logical statements about restrictions of parameter spaces to probabilistic statements about parameters. The method works, but with a lot of caveats: the pivotal variables must be sufficient statistics, must be continuous, &c. Dempster’s explora...

Comparison between fiducial and objective Bayesian inference

R. A. Fisher’s fiducial inference has been the subject of many discussions and controversies ever since he introduced the idea during the 1930’s. The idea experienced a bumpy ride, to say the least, during its early years and one can safely say that it eventually fell into disfavor among mainstream statisticians. However, it appears to have made a resurgence recently under the label of generali...