## The Annals of Mathematical Statistics

### New Methods for Reasoning Towards Posterior Distributions Based on Sample Data

A. P. Dempster

#### Abstract

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.

#### Article information

Source
Ann. Math. Statist., Volume 37, Number 2 (1966), 355-374.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177699517

Digital Object Identifier
doi:10.1214/aoms/1177699517

Mathematical Reviews number (MathSciNet)
MR187357

Zentralblatt MATH identifier
0178.54302

JSTOR