Physical Sciences and Mathematics Commons^™

Need For Techniques Intermediate Between Interval And Probabilistic Ones, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In high performance computing, when we process a large amount of data, we do not have much information about the dependence between measurement errors corresponding to different inputs. To gauge the uncertainty of the result of data processing, the two usual approaches are: the interval approach, when we consider the worst-case scenario in which all measurement errors are strongly correlated, and the probabilistic approach, when we assume that all these errors are independent. The problem is that usually, the interval approach leads to too pessimistic, too large uncertainty estimates, while the probabilistic approach often underestimates the resulting uncertainty. To get …

Why People Tend To Overestimate Joint Probabilities, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that, in general, people overestimate the probabilities of joint events. In this paper, we provide an explanation for this phenomenon -- as explanation based on Laplace Indeterminacy Principle and Maximum Entropy approach.

Need To Combine Interval And Probabilistic Uncertainty: What Needs To Be Computed, What Can Be Computed, What Can Be Feasibly Computed, And How Physics Can Help, Julio Urenda, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In many practical situations, the quantity of interest is difficult to measure directly. In such situations, to estimate this quantity, we measure easier-to-measure quantities which are related to the desired one by a known relation, and we use the results of these measurement to estimate the desired quantity. How accurate is this estimate?

Traditional engineering approach assumes that we know the probability distributions of measurement errors; however, in practice, we often only have partial information about these distributions. In some cases, we only know the upper bounds on the measurement errors; in such cases, the only thing we know about …