Modelling of Dynamic Computer Experiments with Both Qualitative and Quantitative Variables
Computer Experiment , Additive Model , Singular Value Decomposition , Statistical Emulator , Time Series Output , Dynamic Linear Model
Computer experiments are utilized as a popular tool of studying the relationship between responses and the factors that affect them. They are widely used in scientific researches and applications. Dynamic computer experiments refer to computer experiments with time-series responses. Different dynamic computer models have been proposed to emulate the relationship between the time-series responses and the corresponding quantitative factors. Qualitative factors are also widely used and show important effects in many scientific problems. Different models have been proposed for one-dimensional outputs and both quantitative and qualitative factors. In this thesis, we have reviewed some popular dynamic computer models with only quantitative factors. We make empirical comparisons of the prediction accuracy of three existing dynamic computer models with only quantitative factors. Among the three models, the dynamic linear Gaussian process model and the singular value decomposition based Gaussian process model outperform. Based on these two models, we incorporate the qualitative factors utilizing the additive correlation structure and propose two new modelling methods for dynamic computer experiments with both quantitative and qualitative factors. We also explored the different choices of the prior distributions for the unknown parameters in these two models. The prediction accuracy of the two proposed modelling approaches is tested by a limited simulation study.