Computational issues of generalized fiducial inference

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.