Extending NearlyLinear Models
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Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:8290, 2019.
Abstract
NearlyLinear Models are a family of neighbourhood models, obtaining lower/upper probabilities from a given probability by a linear affine transformation with barriers. They include a number of known models as special cases, among them the PariMutuel Model, the $\varepsilon$contamination model, the Total Variation Model and the vacuous lower/upper probabilities. We classified NearlyLinear models, investigating their consistency properties, in previous work. Here we focus on how to extend those NearlyLinear Models that are coherent or at least avoid sure loss. We derive formulae for their natural extensions, interpret a specific model as a natural extension itself of a certain class of lower probabilities, and supply a risk measurement interpretation for one of the natural extensions we compute.
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