Justifying the Principle of Interval Constraints

TL;DR

This paper justifies the Principle of Interval Constraints, which ranks explanations based on expected probability values derived from confidence intervals, using a rigorous classical probability framework and the concept of probabilities of probabilities.

Contribution

It provides a rigorous justification for the Principle of Interval Constraints within the classical probability approach and defends the concept of probabilities of probabilities.

Findings

The principle effectively ranks explanations using interval-based probability estimates.

A rigorous classical framework supports the validity of the principle.

Probabilities of probabilities are defended as a meaningful concept.

Abstract

When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for the probabilities of mutually exclusive and exhaustive explanations. The Principle of Interval Constraints ranks these explanations by determining the expected values of the probabilities based on distributions determined from the interval, constraints. This principle was developed using the Classical Approach to probability. This paper justifies the Principle of Interval Constraints with a more rigorous statement of the Classical Approach and by defending the concept of probabilities of probabilities.