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 Section 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 multinominal sampling with a finite number of contemplated hypotheses. Among the concluding remarks, it is pointed out that the methods of Section 5 include as limiting cases situations with discrete or continuous observable and continuously ranging parameters.
"New Methods for Reasoning Towards Posterior Distributions Based on Sample Data." Ann. Math. Statist. 37 (2) 355 - 374, April, 1966. https://doi.org/10.1214/aoms/1177699517