1,392 research outputs found

    Comment: Expert Elicitation for Reliable System Design

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    Comment: Expert Elicitation for Reliable System Design [arXiv:0708.0279]Comment: Published at http://dx.doi.org/10.1214/088342306000000529 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

    A hybrid Bayesian network for medical device risk assessment and management

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    ISO 14971 is the primary standard used for medical device risk management. While it specifies the requirements for medical device risk management, it does not specify a particular method for performing risk management. Hence, medical device manufacturers are free to develop or use any appropriate methods for managing the risk of medical devices. The most commonly used methods, such as Fault Tree Analysis (FTA), are unable to provide a reasonable basis for computing risk estimates when there are limited or no historical data available or where there is second-order uncertainty about the data. In this paper, we present a novel method for medical device risk management using hybrid Bayesian networks (BNs) that resolves the limitations of classical methods such as FTA and incorporates relevant factors affecting the risk of medical devices. The proposed BN method is generic but can be instantiated on a system-by-system basis, and we apply it to a Defibrillator device to demonstrate the process involved for medical device risk management during production and post-production. The example is validated against real-world data

    Stacking Factorizing Partitioned Expressions in Hybrid Bayesian Network Models

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    Hybrid Bayesian networks (HBN) contain complex conditional probabilistic distributions (CPD) specified as partitioned expressions over discrete and continuous variables. The size of these CPDs grows exponentially with the number of parent nodes when using discrete inference, resulting in significant inefficiency. Normally, an effective way to reduce the CPD size is to use a binary factorization (BF) algorithm to decompose the statistical or arithmetic functions in the CPD by factorizing the number of connected parent nodes to sets of size two. However, the BF algorithm was not designed to handle partitioned expressions. Hence, we propose a new algorithm called stacking factorization (SF) to decompose the partitioned expressions. The SF algorithm creates intermediate nodes to incrementally reconstruct the densities in the original partitioned expression, allowing no more than two continuous parent nodes to be connected to each child node in the resulting HBN. SF can be either used independently or combined with the BF algorithm. We show that the SF+BF algorithm significantly reduces the CPD size and contributes to lowering the tree-width of a model, thus improving efficiency

    Representations of matroids

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    The concept of matroids was originally introduced by Whitney and Van der Waerden in the 1930's to generalise the notion of linear dependence in a vector space; certain axioms satisfied by this relation were observed to be satisfied by other types of ’ dependence’ relations, such as algebraic dependence and ’ cycle’ dependence in a graph. Consequently a matroid was defined to be a set with an abstract dependence relation satisfying these axioms. One of the most natural questions to ask is whether every such ’ matroid' is representable in the obvious sense in a vector space. The answer is of course no (otherwise matroid theory would be equivalent to linear algebra) although in the early years of the subject examples of non-representable matroids were not easily obtainable. In this thesis we continue the work of Inglcton (in [20]) and Vamos (in [35,36]) on the representation problem, buiding up to an algebraic treatment in the important last chapter
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