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Optimal sample planning for system state analysis with partial data collection
Author(s) -
Heller Martin,
Hannig Jan,
Leadbetter Malcolm R.
Publication year - 2015
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.79
Subject(s) - computer science , a priori and a posteriori , sample (material) , heuristic , bayesian probability , inference , data collection , sampling (signal processing) , data mining , bayesian inference , sample size determination , state (computer science) , mathematical optimization , algorithm , artificial intelligence , statistics , mathematics , computer vision , philosophy , chemistry , epistemology , chromatography , filter (signal processing)
We develop optimal and computationally practical procedures to minimize uncertainty concerning the presence of dangerous levels of a contaminant within a building when neither replication nor complete data collection is feasible. More generally, we address inference about the state of a finite system when the state is related to information collected over components of the system when only partial data collection is feasible. When there is no correlation between sample locations, a simple random sample or maximum a priori trait presence would provide optimal sampling choices. When complicated probability models describe trait manifestation, the need to collect only partial data precludes a full fitting of complicated models, and one must rely heavily on prior information naturally leading to a Bayesian approach. Herein, we introduce a computationally efficient heuristic algorithm to simultaneously find optimal sample locations and decision rule parameterizations and then show that it drastically outperforms both random selection and maximum a priori methods. Copyright © 2015 John Wiley & Sons, Ltd.