On the impact of robust statistics on imprecise probability models: A review

Robust statistics is concerned with statistical methods that still lead to reliable conclusions if an ideal model is only approximately true. More recently, the theory of imprecise probabilities was developed as a general methodology to model non-stochastic uncertainty (ambiguity) adequately, and has been successfully applied to many engineering problems. In robust statistics, small deviations from ideal models are modeled by certain neighborhoods. Since nearly all commonly used neighborhoods are imprecise probabilities, a large part of robust statistics can be seen as a special case of imprecise probabilities. Therefore, it seems quite promising to address problems in the theory of imprecise probabilities by trying to generalize results of robust statistics. In this review paper, we present some cases where this has already been done successfully and where the connections between (frequentist) robust statistics and imprecise probabilities are most striking.