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

Abstract

Neighbourhoods of precise probabilities are instrumental to perform robustness analysis, as they rely on very few parameters. In the first part of this study, we introduced a general, unified 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 distances. We finish 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.