| dc.description.abstract | This thesis is concerned with the methodology of smooth emulators for computer experiments. The work in this thesis is categorized into two parts. The first and the main part comprises methods with smooth emulators for the analysis of computer experiments. The second part is devoted to the extension of optimal designs for the smooth emulator. The methodology of the first part is primarily focussed on the problem of less than full rank design model matrix, and we combine the elements of ridge regression with a measure of smoothness to develop an improved emulator. Our analytical results show that mean square error of the parameter of smooth emulator improves over that for the standard regression parameter. We also extend the smooth emulator with the Gaussian process and compare the performance with the Gaussian emulator itself. We have applied our methods to model COVID transmission data as well as to data from simulated climate models. We have concluded from the analytical results and simulated studies that the smooth interpolator outperforms other emulators under certain given conditions which are described in the work. We conclude from the results that smooth emulator is useful particularly in rank deficient design model matrix. In addition, the smooth emulator provides a simple and cheap alternative in situations where Gaussian emulator is not a viable choice. In the second part of this work, we perform a detailed exploratory analysis to find some of the optimal designs for smooth interpolator that provides valuable insights into the properties of the optimal designs for smooth emulator. We also develop analytical results for D- and A-optimal designs for ridge regression not found in literature before. | en_US |
