Purpose: When we know the probability of each model, a natural idea is to select the most probable model. However, in many practical situations, we do not know the exact values of these probabilities, we only know intervals that contain these values. 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: We want the probability-selection method to preserve 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: We describe all techniques for decision making under interval uncertainty about probabilities that are consistent with independence. We prove that these techniques form a 1-parametric family, a family that has already been successfully used in such decision problems.
Originality/value: We provide 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.