Partially specified prior

TL;DR

This paper introduces the concept of a partially specified prior distribution to improve the realism and usefulness of probability statements in post hoc inference problems involving finite populations.

Contribution

It proposes the partially specified prior as a novel approach for making more realistic probability statements in attribute absence decisions.

Findings

Partially specified priors enhance decision-making accuracy.

The approach improves the interpretability of probability statements.

Applicable to finite population sampling scenarios.

Abstract

This note introduces the concept of a partially specified prior distribution for certain post hoc inference problems, where a finite population is sampled once in order to make a decision on the presence or complete absence of some attribute. If the decision is made to accept complete absence, a probability statement may be required that the population is indeed free of the attribute. A partially specified prior is shown to be advantageous in making such statements realistic and useful.