Designing Robust, cost-effective field measurement sets using universal multiple linear regression

Limited monitoring budgets restrict the type and number of sensors that can be installed for field-based studies. Therefore, sensor selection should be both informative and efficient. We propose a method to optimize sensor network design, prior to data collection, by combining multiple linear regression (MLR) and robust decision-making (RDM). Multiple linear regression inherently considers the strength of the relationship between observations and predictions of interest and correlations among proposed observations. In our approach, we use universal Multiple Linear Regression (uMLR) to quantify the explanatory power of all possible combinations of model-simulated candidate observations (of different sensor types and locations). A modelensemble approach allows for network design in the context of user-defined uncertainties, including expected measurement error and parameter and structural uncertainty. Application of uMLR with RDM produces a comprehensive assessment of the likely value of many observation sets. These results can be used to design sensor networks to address specific experimental objectives and to balance the cost and effort of installing sensors to the expected value of the data for model testing and decision support.