## The Annals of Mathematical Statistics

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

#### Citation

Dempster, A. P. New Methods for Reasoning Towards Posterior Distributions Based on Sample Data. Ann. Math. Statist. 37 (1966), no. 2, 355--374. doi:10.1214/aoms/1177699517. https://projecteuclid.org/euclid.aoms/1177699517