Hierarchical Bayes methods for systems with spatially varying condition states

• Published in: Canadian journal of civil engineering Vol. 34; no. 10; pp. 1289 - 1298
• Main Authors: Maes, Marc A, Dann, Markus
• 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: Applied sciences; Bayesian analysis; Bayesian statistical decision theory; Buildings. Public works; Civil engineering; Computation methods. Tables. Charts; Correlation analysis; Decision analysis; Evaluation; Exact sciences and technology; Industrial plants; Infrastructure; Methods; Methods engineering; Project management. Process of design; Spatial analysis (Statistics); Statistical inference; Structural analysis. Stresses; Canada; Markov chain; Monte Carlo method; Spatial distribution; Decision making; Example; Large system; Bayes forecasting; Statistical decision; Hierarchical system; Civil engineering; Method study
• ISSN: 0315-1468; 1208-6029
• DOI: 10.1139/l07-049

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.