How to select a model if we know probabilities with interval uncertainty?

Abstract

Purpose When the probability of each model is known, a natural idea is to select the most probable model. However, in many practical situations, the exact values of these probabilities are not known; only the intervals that contain these values are known. In such situations, a natural idea is to select some probabilities from these intervals and to select a model with the largest selected probabilities. The purpose of this study is to decide how to most adequately select these probabilities. Design/methodology/approach It is desirable to have a probability-selection method that preserves independence. If, according to the probability intervals, the two events were independent, then the selection of probabilities within the intervals should preserve this independence. Findings The paper describes all techniques for decision making under interval uncertainty about probabilities that are consistent with independence. It is proved that these techniques form a 1-parametric family, a family that has already been successfully used in such decision problems. Originality/value This study provides a theoretical explanation of an empirically successful technique for decision-making under interval uncertainty about probabilities. This explanation is based on the natural idea that the method for selecting probabilities from the corresponding intervals should preserve independence.