Complex computer models have extensive usage in scientific and engineering studies. Because the number of computer runs is typically limited, statistical models are used to predict the computer codes. This thesis considers two research problems. The first problem is prediction for computer experiments having quantitative and qualitative mixed input variables. The second is the simultaneous determination of tuning and calibration parameters.
To predict the output from a computer experiment having mixed inputs, we regard the output from a computer experiment code as a realization from a mixture of
Gaussian Stochastic Processes (GaSPs) and have developed two methods. The first
method assumes that the responses at different qualitative input levels share similarities. We build one GaSP model for each level of the qualitative input. Using Bayesian hierarchical models with an empirical prior, the predictions at one qualitative input level are able to borrow information from the responses at other levels. The second method estimates the common trend of the responses at all the qualitative input levels. The prediction is the sum of the estimated average and the predicted deviation of a response from the average. We develop a data adaptive algorithm for the estimation of the common trend to guarantee that the predictive error of this predictor is no bigger than that of a predictor using the data at one level only. We extend the both methods to computer experiments having multiple qualitative inputs.
To simultaneously select tuning and calibration parameters, we develop a Bayesian
discrepancy-based procedure to estimate the tuning parameters and simulate the
estimated posterior distribution of the calibration parameters.
We compare our methodologies with alternatives and implement the methodologies in three biomechanical engineering applications.