Implicit Degree of Support for Finite Lower-Upper Conditional Probabilities Extensions

In this paper we propose a measure for the implicit degree of support for coherent extensions of probabilistic models based on partial conditional lower-upper assessments. This degree of support is induced by the different extension bounds that arise operationally in automated computational inference procedures. These different bounds are induced by the "extreme" distributions compatible with an initial assessment, i.e. those that strictly attain at least one of the constraints imposed by the modeler. The minimum and the maximum of these extension bounds determine the so called "least commitment" coherent extension interval, while the intermediate values can be used to grade the support of the initial assessment for tighter intervals. The appropriateness of the degree of support is determined by coherence of particular sub-intervals of the wider "least commitment" coherent exten- sion range. The proposed degree of support can be helpful in the pro- cess of finding appropriate extension bounds whenever the standard pro- cedure results in bounds that are too wide to be useful.