The Dempster--Shafer calculus for statisticians
International Journal of Approximate Reasoning
On Nonobtuse Simplicial Partitions
SIAM Review
Fiducial inference on the largest mean of a multivariate normal distribution
Journal of Multivariate Analysis
A betting interpretation for probabilities and Dempster--Shafer degrees of belief
International Journal of Approximate Reasoning
A consistent method of estimation for the three-parameter Weibull distribution
Computational Statistics & Data Analysis
Editorial: Special issue on imprecision in statistical data analysis
Computational Statistics & Data Analysis
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Generalized fiducial inference is closely related to the Dempster-Shafer theory of belief functions. It is a general methodology for constructing a distribution on a (possibly vector-valued) model parameter without the use of any prior distribution. The resulting distribution is called the generalized fiducial distribution, which can be applied to form estimates and confidence intervals for the model parameter. Previous studies have shown that such estimates and confidence intervals possess excellent frequentist properties. Therefore it is useful and advantageous to be able to calculate the generalized fiducial distribution, or at least to be able to simulate a random sample of the model parameter from it. For a small class of problems this generalized fiducial distribution can be analytically derived, while for some other problems its exact form is unknown or hard to obtain. A new computational method for conducting generalized fiducial inference without knowing the exact closed form of the generalized fiducial distribution is proposed. It is shown that this computational method enjoys desirable theoretical and empirical properties. Consequently, with this proposed method the applicability of generalized fiducial inference is enhanced.