Abstract :

Simulation models are widely used in various fields including finance, supply chain, health care, biological and human processes in order to analyze the performance and to reproduce the behaviour of complex systems. However, in most cases, the computational simulation is expensive. Simulation metamodeling has been developed to alleviate the computational issue by performing a designed experiment on the computer simulation and developing a predictive distribution.

Nevertheless, as simulation model only serves as a surrogate model for the real system, there still exists a non-negligible discrepancy between the simulation model and the real system, which is referred as model discrepancy. Calibration is a process of adjusting the unknown parameters of the simulation model using observations from a real system, which is very time consuming. The second chapter of this thesis proposes a new metamodeling technique to integrate both simulation data and observations from the real system in order to learn the model inadequacy and predict the performance of the real system. Compared with the traditional metamodelling technique, the proposed new metamodel has been shown to be competitive in terms of prediction accuracy through simulation and analytic results.

In addition, in more general cases, both of the input and output observations from the real system are subjected to noise corruption. Noisy input data are common in many fields, for example, geostatistics and spatial econometric. Accounting for input error on covariates is a well-studied theme in statistics, however, there is a dearth of research on prediction or Gaussian process regression problems in the presence of input error. Gaussian process models do not straightforwardly extend to incorporate input error, and ignoring the input error can lead to poor performance. The third chapter of this thesis proposes a new type of predictor for a Gaussian process with input error. The predictors in the existing literature yields some undesirable properties hence leading to poor prediction performances. Beyond analysing the properties of traditional predictors, this work provides some guidance about how to utilize the advantages of the traditional predictors to achieve better prediction performance.