Uncertainty, Imprecise Probabilities and Interval Capacity Measures on a Product Space
arxiv(2024)
摘要
In Basili and Pratelli (2024), a novel and coherent concept of interval
probability measures has been introduced, providing a method for representing
imprecise probabilities and uncertainty. Within the framework of set algebra,
we introduced the concepts of weak complementation and interval probability
measures associated with a family of random variables, which effectively
capture the inherent uncertainty in any event. This paper conducts a
comprehensive analysis of these concepts within a specific probability space.
Additionally, we elaborate on an updating rule for events, integrating
essential concepts of statistical independence, dependence, and stochastic
dominance.
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