Abstract

The fiducial argument is Fisher’s attempt to make inferential statements about the likely value of parameters without recourse to a specific prior distribution on the parameter space. In its original form using pivotal quantities, the fiducial argument is virtually indistinguishable from Neyman’s theory of confidence intervals. Fisher strove to distance his theory from that of confidence intervals by emphasizing correctly the importance for inference of ancillary statistics and recognizable subsets. Despite many efforts by Fisher, Fraser and Barnard and others over the years, the passage from a pivotal statistic to a probability distribution on the parameter space remains a conceptual stumbling block. In this talk, I will address the question of whether, in any circumstances, parametric inference is possible without a prior distribution. The view initially taken is similar to that of Hora, Buehler, Geisser and Dawid, that inference and prediction are indistinguishable activities. From this point of view, the parameter space is relatively unimportant, and the observation space becomes the focus of inferential activity.

The paper is available at:

http://www.jstor.org/stable/2935559