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EnglishSeveral simplified uncertainty models are derived from a given probability of which they are a perturbation. Among these, we introduced in previous work Nearly-Linear (NL) models. They perform a linear affine transformation of with barriers, obtaining a couple of conjugate lower/upper probabilities, and generalise several well known neighbourhood models. We classified NL models, partitioning them into three subfamilies, and established their basic consistency properties in [5]. In this paper we investigate how to extend NL models that avoid sure loss by means of their natural extension, a basic, although operationally not always simple, inferential procedure in Imprecise Probability Theory. We obtain formulae for computing directly the natural extension in a number of cases, supplying a risk measurement interpretation for one of them. The results in the paper also broaden our knowledge of NL models: we characterise when they avoid sure loss, express some of them as linear (or even convex) combinations of simpler models, and explore relationships with interval probabilities.
| Titolo: | Inference with Nearly-Linear uncertainty models |
| Autori: | |
| Data di pubblicazione: | 2020 |
| Data ahead of print: | 22-apr-2020 |
| Stato di pubblicazione: | Epub ahead of print |
| Rivista: | |
| Abstract: | Several simplified uncertainty models are derived from a given probability of which they are a perturbation. Among these, we introduced in previous work Nearly-Linear (NL) models. They perform a linear affine transformation of with barriers, obtaining a couple of conjugate lower/upper probabilities, and generalise several well known neighbourhood models. We classified NL models, partitioning them into three subfamilies, and established their basic consistency properties in [5]. In this paper we investigate how to extend NL models that avoid sure loss by means of their natural extension, a basic, although operationally not always simple, inferential procedure in Imprecise Probability Theory. We obtain formulae for computing directly the natural extension in a number of cases, supplying a risk measurement interpretation for one of them. The results in the paper also broaden our knowledge of NL models: we characterise when they avoid sure loss, express some of them as linear (or even convex) combinations of simpler models, and explore relationships with interval probabilities. |
| Handle: | http://hdl.handle.net/11368/2965326 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.fss.2020.04.013 |
| URL: | https://www.sciencedirect.com/science/article/pii/S0165011420301287 |
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