In the study of complex physical and engineering processes, it is sometimes either impossible, infeasible or very expensive to observe the actual systems. When such situations arise, computer simulators or codes can be used instead. Often these codes are very complex, requiring many hours or days for a single simulation, and thus the number of times we may implement the code to collect data needs to be as small as possible. The running of such a code at a few chosen input settings comprises a computer experiment. Most of the work done in this area focuses on either estimating the unknown complex input-output relationship or optimizing the output. This thesis considers the problem of percentile estimation in a computer experiments setting.
The input variables are assumed to be independently distributed with known distributions. The output variable is assumed to be related to the input variables through a complex unknown function. Our goal is to estimate, say, the p-th percentile of the induced distribution of the output variable. To achieve this, we propose a sequential-adaptive design algorithm. The responses on the output variable are modeled as realizations of a Gaussian stochastic process. Based on the fitted model, new design sites are selected and added to the existing design. The final set of design points are used to estimate the p-th percentile. The proposed criteria that are used to select new design sites can be thought of as being inspired by the two concepts of statistical inference: confidence interval and hypothesis testing. We present the results obtained from using the sequential--adaptive design methodology, and compare these results to those obtained from fixed design methods.
We also discuss the cases of constrained percentile estimation, and percentile estimation of integrated response functions.