Combining Interval and Probabilistic Uncertainty: What Is Computable?

Abstract

In many practical problems, we need to process measurement results. For example, we need such data processing to predict future values of physical quantities. In these computations, it is important to take into account that measurement results are never absolutely exact, that there is always measurement uncertainty, because of which the measurement re-sults are, in general, somewhat different from the actual (unknown) values of the corresponding quantities. In some cases, all we know about mea-surement uncertainty is an upper bound; in this case, we have an interval uncertainty, meaning that all we know about the actual value is that is belongs to a certain interval. In other cases, we have some information – usually partial – about the corresponding probability distribution. New data processing challenges appear all the time; in many of these cases, it is important to come up with appropriate algorithms for taking uncertainty into account

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