New Methods for Reasoning Towards PosteriorDistributions Based on Sample Data
This paper redefines the concept of sampling from a population with a given parametric form, and thus leads up to some proposed alternatives to the existing Bayesian and fiducial arguments for deriving posterior distributions. Section 2 spells out the basic assumptions of the suggested class of sampling models, and Sect. 3 suggests a mode of inference appropriate to the sampling models adopted. A novel property of these inferences is that they generally assign upper and lower probabilities to events concerning unknowns rather than precise probabilities as given by Bayesian or fiducial arguments. Sections 4 and 5 present details of the new arguments for binomial sampling with a continuous parameter p and for general multinomial sampling with a finite number of contemplated hypotheses. Among the concluding remarks, it is pointed out that the methods of Sect. 5 include as limiting cases situations with discrete or continuous observables and continuously ranging parameters.