Unifying neighbourhood and distortion models: part II - new models and synthesis

Ignacio Montes (1) , Enrique Miranda (1) , Sébastien Destercke (2)

1 Universidad de Oviedo [Oviedo]
2 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

Neighbourhoods of precise probabilities are instrumental to perform robustness analysis, as they rely on very few parameters. In the rst part of this study, we introduced a general, unied view encompassing such neighbourhoods, and revisited some well-known models (pari mutuel, linear vacuous, constant odds-ratio). In this second part, we study models that have received little to no attention, but are induced by classical distances between probabilities, such as the total variation, the Kolmogorov and the L 1 distances. We nish by comparing those models in terms of a number of properties: precision , number of extreme points, n-monotonicity,. .. thus providing possible guidelines to select a neighbourhood rather than another.

Mots clés: Neighbourhood models; distorted probabilities; total variation distance; Kolmogorov distance; L 1 distance

Domaines: Intelligence artificielle [cs.AI]; Probabilités [math.PR]

Ignacio Montes, Enrique Miranda, Sébastien Destercke. Unifying neighbourhood and distortion models: part II - new models and synthesis. International Journal of General Systems, 2020, 49 (6), pp.636-674. ⟨10.1080/03081079.2020.1778683⟩. ⟨hal-02944685⟩