Optimal design for special kernel computer experiments
Seminar Room 1, Newton Institute
AbstractThere are not many exact results for the optimality of experimental designs in the context of space-filling design for computer experiments. In addition there is some disparity between optimal designs for classical regression models, such as D-optimum designs, and designs for Gaussian process models, such as maximum entropy sampling (MES). In both cases one can talk about "kernels". In the first we can think of the regression models as given by kernels. In the second we have a "covariance kernel". There is a link provided by the Karhunen-Loeve expansion of the covariance function. These issues are covered but most time is spent on important design-kernel pairs where there are hard optimality results and design solutions are space-filling in nature. The two main examples covered are multidimensional Fourier models where lattice design are D-optimal and some recent work on Haar wavelets where Sobol sequences are D-optimal.
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