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Title: Bayesian optimal designs for the Gaussian Process Model
Author: Adamou, Maria
ISNI:       0000 0004 5356 6550
Awarding Body: University of Southampton
Current Institution: University of Southampton
Date of Award: 2014
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This thesis is concerned with methodology for finding Bayesian optimal designs for the Gaussian process model when the aim is precise prediction at unobserved points. The fundamental problem addressed is that the design selection criterion obtained from the Bayesian decision theoretic approach is often, in practice, computationally infeasible to apply. We propose an approximation to the objective function in the criterion and develop this approximation for spatial and spatio-temporal studies, and for computer experiments. We provide empirical evidence and theoretical insights to support the approximation. For spatial studies, we use the approximation to find optimal designs for the general sensor placement problem, and also to find the best sensors to remove from an existing monitoring network. We assess the performance of the criterion using a prospective study and also from a retrospective study based on an air pollution dataset. We investigate the robustness of designs to misspecification of the mean function and correlation function in the model through a factorial sensitivity study that compares the performance of optimal designs for the sensor placement problem under different assumptions. In computer experiments, using a Gaussian process model as a surrogate for the output from a computer model, we find optimal designs for prediction using the proposed approximation. A comparison is made of optimal designs obtained from commonly used model-free methods such as the maximin criterion and Latin hypercube sampling via both the space-filling and prediction properties of the designs. For spatio-temporal studies, we extend our proposed approximation to include both space and time dependency and investigate the approximation for a particular choice of separable spatio-temporal correlation function. Two cases are considered: (i) the temporal design is fixed and an optimal spatial design is found; (ii) both optimal temporal and spatial designs are found. For all three of the application areas, we found that the choice of optimal design depends on the degree and the range of the correlation in the Gaussian process model.
Supervisor: Woods, David ; Lewis, Susan ; Sahu, Sujit Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics