Designing experiments for polynomial spline models
Designing experiments for polynomial spline models
Multi-factor B-spline models formed from tensor products, and parsimonous sub-models of these products, are described. Designs are found under these models, with known knot locations, for variance-based criteria (D-, G- and V-optimality) using computer search. Two competing methods of constructing a candidate list are compared and contrasted through examples. The increase in efficiency of these designs compared to standard factorial designs under the B-spline models is demonstrated, and the robustness of the designs to small changes in knot location is discussed. The effectiveness of the models and designs is demonstrated in a case study.
When the number and location of the knots is unknown, variance-based criteria may not be appropriate. Instead, designs can be found by minimising the errors in the predictions that result from model misspecification, or bias. Sufficient conditions are estimated for designs to be all-bias for single factor spline regression, under models built from truncated power bases. For a given set of known knot locations, these designs minimise the bias for assumed models containing any subset of the knots against true models containing this subset and any other distinct subset.
A further level of model uncertainty is introduced by considering an additive contamination term that is assumed to be a realisation of a random variable. This induces a random bias for any given design and assumed model. Prior information on the number of extra knots in the model, their locations and the size of their effects is used to obtain a distribution for the contamination. Design selection criteria are developed for single factor models based upon properties of the bias distribution, including the expectation, variance and median. A computer search technique is used to find designs, where the properties of the bias distribution are estimated by simulation.
University of Southampton
2003
Woods, David Christopher
(2003)
Designing experiments for polynomial spline models.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
Multi-factor B-spline models formed from tensor products, and parsimonous sub-models of these products, are described. Designs are found under these models, with known knot locations, for variance-based criteria (D-, G- and V-optimality) using computer search. Two competing methods of constructing a candidate list are compared and contrasted through examples. The increase in efficiency of these designs compared to standard factorial designs under the B-spline models is demonstrated, and the robustness of the designs to small changes in knot location is discussed. The effectiveness of the models and designs is demonstrated in a case study.
When the number and location of the knots is unknown, variance-based criteria may not be appropriate. Instead, designs can be found by minimising the errors in the predictions that result from model misspecification, or bias. Sufficient conditions are estimated for designs to be all-bias for single factor spline regression, under models built from truncated power bases. For a given set of known knot locations, these designs minimise the bias for assumed models containing any subset of the knots against true models containing this subset and any other distinct subset.
A further level of model uncertainty is introduced by considering an additive contamination term that is assumed to be a realisation of a random variable. This induces a random bias for any given design and assumed model. Prior information on the number of extra knots in the model, their locations and the size of their effects is used to obtain a distribution for the contamination. Design selection criteria are developed for single factor models based upon properties of the bias distribution, including the expectation, variance and median. A computer search technique is used to find designs, where the properties of the bias distribution are estimated by simulation.
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Published date: 2003
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Local EPrints ID: 465124
URI: http://eprints.soton.ac.uk/id/eprint/465124
PURE UUID: 8739d35d-ef8e-4dfd-b11a-ab3933fa79c5
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Date deposited: 05 Jul 2022 00:24
Last modified: 05 Jul 2022 00:24
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Author:
David Christopher Woods
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