Optimal sample planning for system state analysis with partial data collection

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.