Related papers: A note on probability metrics in a categorical set…
The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…
The use of tiered warnings and multicategorical forecasts are ubiquitous in meteorological operations. Here, a flexible family of scoring functions is presented for evaluating the performance of ordered multicategorical forecasts. Each…
This special volume of Statistical Sciences presents some innovative, if not provocative, ideas in the area of reliability, or perhaps more appropriately named, integrated system assessment. In this age of exponential growth in science,…
We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is…
Real-world complex systems often comprise many distinct types of elements as well as many more types of networked interactions between elements. When the relative abundances of types can be measured well, we often observe heavy-tailed…
This paper defines pointwise clustering metrics, a collection of metrics for characterizing the similarity of two clusterings. These metrics have several interesting properties which make them attractive for practical applications. They can…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of…
Probability forecasts are intended to account for the uncertainties inherent in forecasting. It is suggested that from an end-user's point of view probability is not necessarily sufficient to reflect uncertainties that are not simply the…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
Correlation and similarity measures are widely used in all the areas of sciences and social sciences. Often the variables are not numbers but are instead qualitative descriptors called categorical data. We define and study similarity…
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…
The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…
Stochastic models of point patterns in space and time are widely used to issue forecasts or assess risk, and often they affect societally relevant decisions. We adapt the concept of consistent scoring functions and proper scoring rules,…
In this paper, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples. It is possible to define the…
The comparisons of uncertainty calculi from the last two Uncertainty Workshops have all used theoretical probabilistic accuracy as the sole metric. While mathematical correctness is important, there are other factors which should be…
In the report the approach to estimation of quality of planned experiments is considered. This approach is based on the analysis of uncertainty, which will take place under the future hypotheses testing about the existence of a new…
In this paper, we present a formal quantification of epistemic uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions of differential equations contain inherent uncertainties due…
In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution…