Multivariate Models and Confidence Intervals: A Local Random Set Approach

This article is devoted to the propagation of families of confidence intervals obtained by non-parametric methods through multivariate functions comprising the semantics of confidence limits. At fixed confidence level, local random sets are defined whose aggregation admits the calculation of upper probabilities of events. In the multivariate case, a number of ways of combinations is highlighted to encompass independence and unknown interaction using random set independence and Frechet bounds. For all cases we derive formulas for the corresponding upper probabilities and elaborate how they relate. The methods are exemplified by means of an example from structural mechanics.