Hierarchical Bayes methods for systems with spatially varying condition states
In engineering decision making, we often face problems where the conditions governing certain response models vary spatially. In such cases, the use of hierarchical Bayesian models is often beneficial. Such models are based on a "condition state" vector that is assumed to be conditionally...
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Published in | Canadian journal of civil engineering Vol. 34; no. 10; pp. 1289 - 1298 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Ottawa, Canada
NRC Research Press
01.10.2007
National Research Council of Canada Canadian Science Publishing NRC Research Press |
Subjects | |
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Abstract | In engineering decision making, we often face problems where the conditions governing certain response models vary spatially. In such cases, the use of hierarchical Bayesian models is often beneficial. Such models are based on a "condition state" vector that is assumed to be conditionally independent given a set of "hyper-parameters." All other process parameters are then conditional on this state variable vector. Such models can be applied to a large variety of problems where data from various systems or sources need to be spatially "mixed," such as in deteriorating infrastructure, spatial aspects of corrosion, preference and consequence modeling, and system failure models for large industrial plants. The models are especially useful for performing statistical inference and for updating in the context of life-cycle optimization, optimal inspection, and maintenance planning. A detailed extension is explored that allows for the spatial correlation of the individual "states" given the hyper-parameters. This allows an efficient posterior assessment of high-level upcrossing rates for the purpose of risk analysis.Key words: spatially distributed processes, hierarchical Bayes models, statistical inference for large systems, spatial correlation. |
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AbstractList | In engineering decision making, we often face problems where the conditions governing certain response models vary spatially. In such cases, the use of hierarchical Bayesian models is often beneficial. Such models are based on a 'condition state' vector that is assumed to be conditionally independent given a set of 'hyper-parameters.' All other process parameters are then conditional on this state variable vector. Such models can be applied to a large variety of problems where data from various systems or sources need to be spatially 'mixed,'such as in deteriorating infrastructure, spatial aspects of corrosion, preference and consequence modeling, and system failure models for large industrial plants. The models are especially useful for performing statistical inference and for updating in the context of life-cycle optimization, optimal inspection, and maintenance planning. A detailed extension is explored that allows for the spatial correlation of the individual 'states' given the hyper-parameters. This allows an efficient posterior assessment of high-level upcrossing rates for the purpose of risk analysis. In engineering decision making, we often face problems where the conditions governing certain response models vary spatially. In such cases, the use of hierarchical Bayesian models is often beneficial. Such models are based on a “condition state” vector that is assumed to be conditionally independent given a set of “hyper-parameters.” All other process parameters are then conditional on this state variable vector. Such models can be applied to a large variety of problems where data from various systems or sources need to be spatially “mixed,” such as in deteriorating infrastructure, spatial aspects of corrosion, preference and consequence modeling, and system failure models for large industrial plants. The models are especially useful for performing statistical inference and for updating in the context of life-cycle optimization, optimal inspection, and maintenance planning. A detailed extension is explored that allows for the spatial correlation of the individual “states” given the hyper-parameters. This allows an efficient posterior assessment of high-level upcrossing rates for the purpose of risk analysis.Key words: spatially distributed processes, hierarchical Bayes models, statistical inference for large systems, spatial correlation. In engineering decision making, we often face problems where the conditions governing certain response models vary spatially. In such cases, the use of hierarchical Bayesian models is often beneficial. Such models are based on a "condition state" vector that is assumed to be conditionally independent given a set of "hyper-parameters." All other process parameters are then conditional on this state variable vector. Such models can be applied to a large variety of problems where data from various systems or sources need to be spatially "mixed," such as in deteriorating infrastructure, spatial aspects of corrosion, preference and consequence modeling, and system failure models for large industrial plants. The models are especially useful for performing statistical inference and for updating in the context of life-cycle optimization, optimal inspection, and maintenance planning. A detailed extension is explored that allows for the spatial correlation of the individual "states" given the hyper-parameters. This allows an efficient posterior assessment of high-level upcrossing rates for the purpose of risk analysis. [PUBLICATION ABSTRACT] |
Abstract_FL | Lors de la prise de décisions d'ingénierie, nous sommes souvent confrontés à des problèmes pour lesquels les conditions régissant certains modèles de réponse varient dans l'espace. Dans de tels cas, il est souvent bénéfique d'utiliser les modèles hiérarchiques bayesiens. Ces modèles sont basés sur un vecteur « d'état » qui est présumé conditionnellement indépendant pour un ensemble « d'hyper-paramètres » choisi. Tous les autres paramètres du procédé dépendent ensuite de ce vecteur variable d'état. De tels modèles peuvent être utilisés sur une grande plage de problèmes où les données provenant de divers systèmes ou sources doivent être « mélangées » dans l'espace, comme dans le cas d'une infrastructure se détériorant, les aspects spatiaux de la corrosion, la modélisation des préférences et des conséquences, ainsi que les modèles de défaillance des systèmes pour les grandes usines industrielles. Les modèles sont particulièrement utiles pour réaliser une inférence statistique ainsi que pour les mises à jour dans le contexte d'optimisation du cycle de vie, d'inspection optimale et de planification de la maintenance. Une extension détaillée est étudiée qui permet la corrélation spatiale des « états » individuels pour les hyper-paramètres donnés. Cela permet une évaluation efficace a posteriori des taux élevés de passages ascendants (« upcrossing ») aux fins d'analyse des risques.Mots-clés : procédés distribués dans l'espace, modèles hiérarchiques bayesiens, inférence statistique de grands systèmes, corrélation spatiale.[Traduit par la Rédaction] |
Audience | Academic |
Author | Maes, Marc A Dann, Markus |
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References | Maes M.A. (p_13/p_13_1) 2003; 23 Faber M.H. (p_6/p_6_1) 2006; 21 Vaurio J.K. (p_21/p_21_1) 1987; 17 Borsuk M. (p_2/p_2_1) 2001; 143 Maes M.A. (p_12/p_12_1) 2002; 124 Bunea C. (p_3/p_3_1) 2005; 90 Hofer E. (p_9/p_9_1) 1999; 67 Maes M.A. (p_14/p_14_1) 2006; 91 |
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Title | Hierarchical Bayes methods for systems with spatially varying condition states |
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