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.
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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. Part 1 Reasoning and behaviour: interpretations of probability beliefs and behaviour inference and decision reasoning and rationality assessment strategies survey of related work. Part 2 Coherent previsions: possibility probability currency upper and lower previsions avoiding sure loss coherence basic properties of coherent previsions coherent probabilities linear previsions and additive probabilities examples of coherent previsions interpretations of prevision and probability objections to behavioural theories of probability. Part 3 Extensions, envelopes and decisions: natural extension extension from a field lower envelopes of linear previsions linear extension invariant linear previsions compactness and extreme points of M(P) desirability and preference equivalent models for beliefs decision making. Part 4 Assessment and elicitation: a general elicitation procedure finitely-generated models and simplex representations steps in assessment process classificatory probability comparative probability other types of assessment. Part 5 The importance of imprecision: uncertainty, indeterminacy and imprecision sources from imprecision information from Bernoulli trials prior-data conflict Bayesian noninformative prioirs indecision axioms of precision practical reasons for precision Bayesian sensitivity analysis second-order probabilities fuzzy sets maximum entropy the Dempster-Shafer theory of belief functions. Part 6 Conditional previsions: updated and contingent previsions separate coherence coherence with unconditional previsions the generalized Bayes rule coherence axioms examples of conditional previsions extension of conditional and marginal previsions conglomerability countable additivity conditioning on events of probability zero updating beliefs. Part 7 Coherent statistical models: general concepts of coherence sampling models coherence of sampling model and posterior previsions inferences from improper priors confidence intervals and relevant subsets proper prior previsions standard Bayesian inference inferences from imprecise priors joint prior previsions. Part 8 Statistical reasoning: a general theroy of natural extension extension to prior previsions extension to predictive previsions extension to posterior previsions posteriors for imprecise sampling models the likelihood principle. Part 9 Structural judgements: independent events independent experiments constructing joint previsions from independent marginals permutability exchangeability Robust Bernoulli models structural judgements. Appendices: verifying coherence N-coherence win and place betting on horses topological structure and L and P separating hyperplane theorems desirability upper and lower variances operational measuremnet procedures the World Cup football experiment regular extension W-coherence. This article reviews statistical techniques for combining multiple probability distributions. The framework is that of a decision maker who consults several experts regarding some events. The experts express their opinions in the form of probability distributions. The decision maker must aggregate the experts' distributions into a single distribution that can be used for decision making. Two classes of aggregation methods are reviewed. When using a supra Bayesian procedure, the decision maker treats the expert opinions as data that may be combined with its own prior distribution via Bayes' rule. When using a linear opinion pool, the decision maker forms a linear combination of the expert opinions. The major feature that makes the aggregation of expert opinions difficult is the high correlation or dependence that typically occurs among these opinions. A theme of this paper is the need for training procedures that result in experts with relatively independent opinions or for aggregation methods that implici... In this work, we present a novel approach to clustering Web site users into different groups and generating common user profiles. These profiles can be used to make recommendations, personalize Web sites, and for other uses such as targeting users for advertising. By using the concept of mass distribution in Dempster-Shafer's theory, the belief function similarity measure in our algorithm adds to the clustering task the ability to capture the uncertainty among Web user's navigation behavior. Our algorithm is relatively simple to use and gives comparable results to other approaches reported in the literature of web mining. A method for the classification of land cover in urban areas by the fusion of first and last pulse LIDAR data and multi-spectral images is presented. Apart from buildings, the classes "tree", "grass land", and "bare soil" are also distinguished by a classification method based on the theory of Dempster-Shafer for data fusion. Examples are given for a test site in Germany. This paper proposes a multimodal biometric system through Gaussian Mixture Model (GMM) for face and ear biometrics with belief fusion of the estimated scores characterized by Gabor responses and the proposed fusion is accomplished by Dempster-Shafer (DS) decision theory. Face and ear images are convolved with Gabor wavelet filters to extracts spatially enhanced Gabor facial features and Gabor ear features. Further, GMM is applied to the high-dimensional Gabor face and Gabor ear responses separately for quantitive measurements. Expectation Maximization (EM) algorithm is used to estimate density parameters in GMM. This produces two sets of feature vectors which are then fused using Dempster-Shafer theory. Experiments are conducted on two multimodal databases, namely, IIT Kanpur database and virtual database. Former contains face and ear images of 400 individuals while later consist of both images of 17 subjects taken from BANCA face database and TUM ear database. It is found that use of Gabor wavelet filters along with GMM and DS theory can provide robust and efficient multimodal fusion strategy. Different formalisms for solving problems of inference under uncertainty have been developed so far. The most popular numerical approach is the theory of Bayesian inference [Lauritzen and Spiegelhalter, 1988]. More general approaches are the Dempster-Shafer theory of evidence [Shafer, 1976], and possibility theory [Dubois and Prade, 1990], which is closely related to fuzzy systems. For these systems computer implementations are available. In competition with these numerical methods are different symbolic approaches. Many of them are based on different types of non-monotonic logic. A method is proposed to quantify uncertainty on statistical forecasts using the formalism of belief functions. The approach is based on two steps. In the estimation step, a belief function on the parameter space is constructed from the normalized likelihood given the observed data. In the prediction step, the variable Y to be forecasted is written as a function of the parameter θ and an auxiliary random variable Z with known distribution not depending on the parameter, a model initially proposed by Dempster for statistical inference. Propagating beliefs about θ and Z through this model yields a predictive belief function on Y. The method is demonstrated on the problem of forecasting innovation diffusion using the Bass model, yielding a belief function on the number of adopters of an innovation in some future time period, based on past adoption data. The increasing number of ontologies of the semantic web poses new challenges for ontology mapping. Ontology mapping in the context of question answering can provide more correct results if the mapping process can deal with uncertainty effectively that is caused by the incomplete and inconsistent information used and produced by the mapping process. We present a novel approach of how Dempster-Shafer belief functions can be used to represent uncertain similarities created by both syntactic and semantic similarity algorithms. For ontology mapping in the context of question answering on the semantic web we propose a multi agent framework where agents create dynamic ontology mappings in order to integrate information and provide precise answers for the users query. We also discuss the problems which can be encountered if we have conflicting beliefs between agents in a particular mapping. This paper concerns the combination of experts' probability distributions in risk analysis, discussing a variety of combination methods and attempting to highlight the important conceptual and practical issues to be considered in designing a combination process in practice. The role of experts is important because their judgments can provide valuable information, particularly in view of the limited availability of “hard data” regarding many important uncertainties in risk analysis. Because uncertainties are represented in terms of probability distributions in probabilistic risk analysis (PRA), we consider expert information in terms of probability distributions. The motivation for the use of multiple experts is simply the desire to obtain as much information as possible. Combining experts' probability distributions summarizes the accumulated information for risk analysts and decision-makers. Procedures for combining probability distributions are often compartmentalized as mathematical aggregation methods or behavioral approaches, and we discuss both categories. However, an overall aggregation process could involve both mathematical and behavioral aspects, and no single process is best in all circumstances. An understanding of the pros and cons of different methods and the key issues to consider is valuable in the design of a combination process for a specific PRA. The output, a “combined probability distribution,” can ideally be viewed as representing a summary of the current state of expert opinion regarding the uncertainty of interest. This thesis presents a logical formalism for representing and reasoning with probabilistic knowledge. The formalism differs from previous efforts in this area in a number of ways. Most previous work has investigated ways of assigning probabilities to the sentences of a logical language. Such an assignment fails to capture an important class of probabilistic assertions, empirical generalizations. Such generalizations are particularly important for AI, since they can be accumulated through experience with the world. Thus, they offer the possibility of reasoning in very general domains, domains where no experts are available to gather subjective probabilities from. A logic is developed which can represent these empirical generalizations. Reasoning can be performed through a proof theory which is shown to be sound and complete. Furthermore, the logic can represent and reason with a very general set of assertions, including many non-numeric assertions. This also is important for AI as numbers are usually not available. The logic makes it clear that there is an essential difference between empirical, or statistical, probabilities and probabilities assigned to sentences, e.g., subjective probabilities. The second part of the formalism is an inductive mechanism for assigning degrees of belief to sentences based on the empirical generalizations expressed in the logic. these degrees of belief have a strong advantage over subjective probabilities: they are founded on objective statistical knowledge about the world. Furthermore, the mechanism of assigning degrees of belief gives a natural answer to the question "Where do the probabilities come from:" they come from our experience with the world. The two parts of the formalism offer combined, interacting, but still clearly separated, plausible inductive inference and sound deductive inference. Statistical aggregation is often used to combine multiple opinions within a group. Such aggregates outperform individuals, including experts, in various prediction and estimation tasks. This result is attributed to the “wisdom of crowds.” We seek to improve the quality of such aggregates by eliminating poorly performing individuals from the crowd. We propose a new measure of contribution to assess the judges' performance relative to the group and use positive contributors to build a weighting model for aggregating forecasts. In Study 1, we analyze 1,233 judges forecasting almost 200 current events to illustrate the superiority of our model over unweighted models and models weighted by measures of absolute performance. In Study 2, we replicate our findings by using economic forecasts from the European Central Bank and show how the method can be used to identify smaller crowds of the top positive contributors. We show that the model derives its power from identifying experts who consistently outperform the crowd. Data, as supplemental material, are available at http: dx.doi.org 10.1287 mnsc.2014.1909 . This paper was accepted by James Smith, decision analysis. The majority of existing automatic mine detection algorithms which have been developed are robust at detecting mine-like objects (MLOs) at the expense of detecting many false alarms. These objects must later be classified as mine or not-mine. The authors present a model based technique using Dempster–Shafer information theory to extend the standard mine not-mine classification procedure to provide both shape and size information on the object. A sonar simulator is used to produce synthetic realisations of mine-like object shadow regions which are compared to those of the unknown object using the Hausdorff distance. This measurement is fused with other available information from the object's shadow and highlight regions to produce a membership function for each of the considered object classes. Dempster–Shafer information theory is used to classify the objects using both mono-view and multi-view analysis. In both cases, results are presented on real data. This paper begins by presenting a simple model of the way in which experts estimate probabilities. The model is then used to construct a likelihood-based aggregation formula for combining multiple probability forecasts. The resulting aggregator has a simple analytical form that depends on a single, easily-interpretable parameter. This makes it computationally simple, attractive for further development, and robust against overfitting. Based on a large-scale dataset in which over 1300 experts tried to predict 69 geopolitical events, our aggregator is found to be superior to several widely-used aggregation algorithms. We examine the problem of constructing and maintaining a map of an autonomous vehicle's environment for the purpose of navigation, using evidential reasoning. The inherent uncertainty in the origin of measurements of sensors demands a probabilistic approach to processing, or fusing, the new sensory information to build an accurate map. In the paper, the map is based on a two-dimensional (2-D) occupancy grid. The sensor readings are fused into the map using the Dempster-Shafer inference rule. This evidential approach with its multivalued hypotheses allows quantitative analysis of the quality of the data. The map building system is experimentally evaluated using sonar data from real environments. In this paper we present a generalization of the ASPIC ar- gumentation system, where a rule can be associated with a probability. This probability expresses uncertainty about whether or not the partic- ular rule is active. We call this system p-ASPIC. The uncertainty about rules carries over to uncertainty about whether or not a particular argu- ment is active. We generalize the usual Dung-style abstract argumenta- tion semantics, in order to deal with this uncertainty. Our work should be understood as an initial step in the direction of probabilistic, instan- tiated, Dung-style argumentation, and we discuss a number of directions for future work. The aggregate prediction from a group of forecasters often outperformsthe individual forecasts from experts. In this paper, wepresent an improvement on the traditional “Wisdom of Crowds” aggregation technique that uses extra information elicited fromforecasters along with their prediction. An analysis of 64 forecastingquestions answered by a group of 1000+ novice predictorsshows that applying heuristic weighting rules to forecasts resultsin a 28 improvement in the accuracy of the group’s predictions.