71,139 research outputs found

    Epistemic Modal Credence

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    Triviality results threaten plausible principles governing our credence in epistemic modal claims. This paper develops a new account of modal credence which avoids triviality. On the resulting theory, probabilities are assigned not to sets of worlds, but rather to sets of information state-world pairs. The theory avoids triviality by giving up the principle that rational credence is closed under conditionalization. A rational agent can become irrational by conditionalizing on new evidence. In place of conditionalization, the paper develops a new account of updating: conditionalization with normalization

    Using graphical models and multi-attribute utility theory for probabilistic uncertainty handling in large systems, with application to nuclear emergency management

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    Although many decision-making problems involve uncertainty, uncertainty handling within large decision support systems (DSSs) is challenging. One domain where uncertainty handling is critical is emergency response management, in particular nuclear emergency response, where decision making takes place in an uncertain, dynamically changing environment. Assimilation and analysis of data can help to reduce these uncertainties, but it is critical to do this in an efficient and defensible way. After briefly introducing the structure of a typical DSS for nuclear emergencies, the paper sets up a theoretical structure that enables a formal Bayesian decision analysis to be performed for environments like this within a DSS architecture. In such probabilistic DSSs many input conditional probability distributions are provided by different sets of experts overseeing different aspects of the emergency. These probabilities are then used by the decision maker (DM) to find her optimal decision. We demonstrate in this paper that unless due care is taken in such a composite framework, coherence and rationality may be compromised in a sense made explicit below. The technology we describe here builds a framework around which Bayesian data updating can be performed in a modular way, ensuring both coherence and efficiency, and provides sufficient unambiguous information to enable the DM to discover her expected utility maximizing policy

    Updating beliefs with incomplete observations

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    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

    Another Approach to Consensus and Maximally Informed Opinions with Increasing Evidence

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    Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling
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