D-Optimal Design for Nested Sensor Placement

Sudell, David and Killick, Rebecca and Titman, Andrew (2024) D-Optimal Design for Nested Sensor Placement. PhD thesis, Lancaster University.

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Abstract

This thesis introduces a new method for the construction of D-optimal designs with a nesting restriction on the choice of design points. It is motivated by an industrial problem in sensor placement for flood monitoring, although the applications to experiment design are not restricted to this field. The nesting structure has two levels. Design points occupy the lower level, and each design point is required to be associated with precisely one member of the higher level. An adaptation of an existing pairwise swap algorithm, sometimes called the Fedorov algorithm, is made to suit this nesting requirement for static linear models. The adaptation features swap operations at the higher level of the nesting structure as well as at the lower level. The performance of this method is demonstrated using simulated and application datasets. Further adaptations are then made to allow for Poisson models, employing a Gaussian quadrature method to effect a Bayesian design. Changes in design points over time are also made possible using applications of the algorithm for the linear model case. The primary motivation across all of the new methodology and its applications is the use of remote sensors in the natural environment as part of the Internet of Things.