Pointwise bias error bounds for response surface approximations and min-max bias design
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Papila, Melih and Haftka, Raphael T. and Watson, Layne T. (2005) Pointwise bias error bounds for response surface approximations and min-max bias design. AIAA Journal, 43 (8). pp. 1797-1807. ISSN 0001-1452
Two approaches addressing response surface approximation errors due to model inadequacy
(bias error) are presented, and a design of experiments minimizing the maximal bias error
is proposed. Both approaches assume that the functional form of the true model is known and
seek, at each point in design space, worst case bounds on the absolute error. The rst approach is
implemented prior to data generation. This data independent error bound can identify locations in
the design space where the accuracy of the approximation tted on a given design of experiments
may be poor. The data independent error bound can easily be implemented in a search for a
design of experiments that minimize the bias error bound as it requires very little computation.
The second approach is to be used posterior to the data generation and provides tightened error
bound consistent with the data. This data dependent error bound requires the solution of two
linear programming problems at each point. The paper demonstrates the data independent error
bound for design of experiments of two-variable examples. Randomly generated polynomials in
two variables are then used to validate the data dependent bias-error bound distribution.
|Subjects:||Q Science > QA Mathematics|
|Deposited By:||Melih Papila|
|Deposited On:||07 Oct 2005 03:00|
|Last Modified:||22 Nov 2007 17:05|
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