In this paper, computational aspects of the panel aggregation problem are addressed. Motivated primarily by applications of risk assessment, an algorithm is developed for aggregating large corpora of internally incoherent probability assessments. The algorithm is characterized by a provable performance guarantee, and is demonstrated to be orders of magnitude faster than existing tools when tested on several real-world data-sets. In addition, unexpected connections between research in risk assessment and wireless sensor networks are exposed, as several key ideas are illustrated to be useful in both fields.
Finally, proponents of Dempster-Shafer theory @cite_7 (and associated fusion rules) object to probability as an idiom for belief, in part because of its inability to distinguish uncertainty from ignorance. The merits of Dempster-Shafer aside, one could argue for abstention as an expression of ignorance. As the preceding examples illustrate, even abstaining experts may disagree (i.e., experts' forecasts may be mutually incoherent), and therefore the panel aggregation problem remains. Thus, CAP is a natural aggregation principle in the setting where judges express uncertainty with probability and ignorance through abstention, and thereby extends the utility of probabilistic forecasts by affording experts more expressive beliefs with abstention.
@cite_7
2797148637
We propose an extended relational database model which can model both uncertainty and imprecision in data. This model is based on Dempster-Shafer theory which has become popular in AI as an uncertainty reasoning tool. The definitions of Be1 and Pls functions in Dempster-Shafer theory are extended to compute the beliefs of various comparisons (e.g., equality, less than, etc.) between two basic probability assignments. Based on these new definitions of Be1 and Pls functions and the Boolean combinations of Be1 and Pls values for two events, five relational operators such as Select, Cartesian Product, Join, Projection Intersect, and Union are defined. From the Publisher: Probabilistic Reasoning in Intelligent Systems is a complete andaccessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertaintyand offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognitionin short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information. Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability. We first describe a metric for uncertain probabilities called opinion, and subsequently a set of logical operators that can be used for logical reasoning with uncertain propositions. This framework which is called subjective logic uses elements from the Dempster-Shafer belief theory and we show that it is compatible with binary logic and probability calculus. Abstract We present a measure of performance (MOP) for identification algorithms based on the evidential theory of Dempster–Shafer. As an MOP, we introduce a principled distance between two basic probability assignments (BPAs) (or two bodies of evidence) based on a quantification of the similarity between sets. We give a geometrical interpretation of BPA and show that the proposed distance satisfies all the requirements for a metric. We also show the link with the quantification of Dempster's weight of conflict proposed by George and Pal. We compare this MOP to that described by Fixsen and Mahler and illustrate the behaviors of the two MOPs with numerical examples.