Reliable Uncertain Evidence Modeling in Bayesian Networks by Credal Networks

A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard updating in an augmented credal network, equivalent to a set of consistent Bayesian networks. A characterization of the computational complexity for this task is derived together with an efficient exact procedure for a subclass of instances. In the case of multiple uncertain evidences over the same variable, the proposed procedure can provide a set-valued version of the geometric approach to opinion pooling.Comment: 19 page

Updating beliefs with incomplete observations

Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete. This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently, Grunwald and Halpern have shown that commonly used updating strategies fail in this case, except under very special assumptions. In this paper we propose a new method for updating probabilities with incomplete observations. Our approach is deliberately conservative: we make no assumptions about the so-called incompleteness mechanism that associates complete with incomplete observations. We model our ignorance about this mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities, and we use only coherence arguments to turn prior into posterior probabilities. In general, this new approach to updating produces lower and upper posterior probabilities and expectations, as well as partially determinate decisions. This is a logical consequence of the existing ignorance about the incompleteness mechanism. We apply the new approach to the problem of classification of new evidence in probabilistic expert systems, where it leads to a new, so-called conservative updating rule. In the special case of Bayesian networks constructed using expert knowledge, we provide an exact algorithm for classification based on our updating rule, which has linear-time complexity for a class of networks wider than polytrees. This result is then extended to the more general framework of credal networks, where computations are often much harder than with Bayesian nets. Using an example, we show that our rule appears to provide a solid basis for reliable updating with incomplete observations, when no strong assumptions about the incompleteness mechanism are justified.Comment: Replaced with extended versio

The Effect of Communicating Ambiguous Risk Information on Choice

Decision makers are frequently confronted with ambiguous risk information about activities with potential hazards. This may be a result of conflicting risk estimates from multiple sources or ambiguous risk information from a single source. The paper considers processing ambiguous risk information and its effect on the behavior of a decision maker with a-maximin expected utility preferences. The effect of imprecise risk information on behavior is related to the content of information, the decision maker’s trust in different sources of information, and his or her aversion to ambiguity.a-Maximin Expected Utility, aggregation of expert opinions, ambiguity, Knightian uncertainty, risk communication, trust in information source, Risk and Uncertainty,

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Advanced Bayesian networks for reliability and risk analysis in geotechnical engineering

The stability and deformation problems of soil have been a research topic of great concern since the past decades. The potential catastrophic events are induced by various complex factors, such as uncertain geotechnical conditions, external environment, and anthropogenic influence, etc. To prevent the occurrence of disasters in geotechnical engineering, the main purpose of this study is to enhance the Bayesian networks (BNs) model for quantifying the uncertainty and predicting the risk level in solving the geotechnical problems. The advanced BNs model is effective for analyzing the geotechnical problems in the poor data environment. The advanced BNs approach proposed in this study is applied to solve the stability of soil slopes problem associated with the specific-site data. When probabilistic models for soil properties are adopted, enhanced BNs approach was adopted to cope with continuous input parameters. On the other hand, Credal networks (CNs), developed on the basis of BNs, are specially used for incomplete input information. In addition, the probabilities of slope failure are also investigated for different evidences. A discretization approach for the enhanced BNs is applied in the case of evidence entering into the continuous nodes. Two examples implemented are to demonstrate the feasibility and predictive effectiveness of the BNs model. The results indicate the enhanced BNs show a precisely low risk for the slope studied. Unlike the BNs, the results of CNs are presented with bounds. The comparison of three different input information reveals the more imprecision in input, the more uncertainty in output. Both of them can provide the useful disaster-induced information for decision-makers. According to the information updating in the models, the position of the water table shows a significant role in the slope failure, which is controlled by the drainage states. Also, it discusses how the different types of BNs contribute to assessing the reliability and risk of real slopes, and how new information could be introduced in the analysis. The proposed models in this study illustrate the advanced BN model is a good diagnosis tool for estimating the risk level of the slope failure. In a follow-up study, the BNs model is developed based on its potential capability for the information updating and importance measure. To reduce the influence of uncertainty, with the proposed BN model, the soil parameters are updated accurately during the excavation process, and besides, the contribution of epistemic uncertainty from geotechnical parameters to the potential disaster can be characterized based on the developed BN model. The results of this study indicate the BNs model is an effective and flexible tool for risk analysis and decision making support in geotechnical engineering

Logics of Imprecise Comparative Probability

This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability andcomparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures

Generalized belief change with imprecise probabilities and graphical models

We provide a theoretical investigation of probabilistic belief revision in complex frameworks, under extended conditions of uncertainty, inconsistency and imprecision. We motivate our kinematical approach by specializing our discussion to probabilistic reasoning with graphical models, whose modular representation allows for efficient inference. Most results in this direction are derived from the relevant work of Chan and Darwiche (2005), that first proved the inter-reducibility of virtual and probabilistic evidence. Such forms of information, deeply distinct in their meaning, are extended to the conditional and imprecise frameworks, allowing further generalizations, e.g. to experts' qualitative assessments. Belief aggregation and iterated revision of a rational agent's belief are also explored