Extending Nearly-Linear Models
Abstract
Nearly-Linear 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 Pari-Mutuel Model, the $\varepsilon$-contamination model, the Total Variation Model and the vacuous lower/upper probabilities. We classified Nearly-Linear models, investigating their consistency properties, in previous work. Here we focus on how to extend those Nearly-Linear 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.
Cite
Text
Corsato et al. "Extending Nearly-Linear Models." Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, 2019.Markdown
[Corsato et al. "Extending Nearly-Linear Models." Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, 2019.](https://mlanthology.org/isipta/2019/corsato2019isipta-extending/)BibTeX
@inproceedings{corsato2019isipta-extending,
title = {{Extending Nearly-Linear Models}},
author = {Corsato, Chiara and Pelessoni, Renato and Vicig, Paolo},
booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications},
year = {2019},
pages = {82-90},
volume = {103},
url = {https://mlanthology.org/isipta/2019/corsato2019isipta-extending/}
}