The paper describes an approach to representing, aggregating and propagating aleatory and epistemic uncertainty through computational models. The approach was developed in part under the Epistemic Uncertainty Project formed at Sandia National Laboratories, USA, to investigate the applicability and usefulness of some of the modern mathematical theories for the representation of different types of uncertainty, and came out as a result of collaboration with Saint Petersburg Forest Technical Academy, Russia, and personally with L. Utkin. Different aspects of the approach can be found in [l]-[3]. In general terms, the approach can be delineated as follows. It is presupposed that the parameter of interest is a random variable governed by a probability distribution which is unknown. Epistemic uncertainty is modeled by adopting a set of admissible probability distributions matching the existing information. The modeler has no grounds for preferring any one of these distributions over another. In the marginal case of complete ignorance, the set of admissible distributions coincides with the set of all possible probability distributions. Statistical information concerning the random variable of interest is regarded as complete if the distribution is known precisely. Otherwise the information is partial. Partial knowledge is modeled by providing a set of admissible probability distributions that is a subset of the set of all possible probability distributions. In practice it is not necessary to judge directly on probability distributions and their parameters but on any probability characteristics that can in principle be computed as functions of admitted distributions. In such a case, any judgment/evidence imposes constraints on the set of distributions shaping the admissible set. The more (non-conflicting) statistical evidence the analyst has at hand, the smaller the admissible set. Judgments are considered conflicting if they cut off in the set of all possible probability distributions non-intersecting subsets. Conflicting evidence can also be aggregated, but this will expand the set of admissible distributions. Dealing with the sets of probability distributions results in imprecise probability characteristics calculated over these sets. Lower and upper bounds of probability characteristics can be propagated through systems with known mappings between the inputs and outputs. Different sources of evidence on the input parameters (precise, imprecise, and aleatorically or epistemically uncertain) can be combined and explicitly seen in the outputs after being propagated. Modeling epistemic uncertainty by admissible sets of probability distributions makes epistemic and aleatory models compatible, for aleatory uncertainty is modeled by precise probability distributions. What follows is a demonstration of how the above statements can be applied.
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