Statistical Approaches for Computer Experiments, Management of Temperature Control Systems, and Prediction of Dose-Responses

The issues of collecting data from and building better emulators for computer experiments are addressed. In addition, predictive models for temperature control systems and dose-response curves are explored. Computer experiments are computationally expensive, deterministic simulations of real systems and are frequently used in climatology, systems biology, and engineering. A class of sequences of nested space-filling designs for collecting data from ensembles of computer experiments with multiple levels of accuracy and expense is proposed. These designs have good space-filling properties and are available for continuous, discrete, or mixed inputs. A multi-scale procedure originally proposed in applied mathematics for improving the accuracy of computer experiment emulators is examined. The error is separated into nominal and numeric contributions and bounds for each are derived. A multi-variate Gaussian autoregressive hidden Markov model with periodic transition matrix is proposed for the predictive modeling of large temperature control systems. The performance of the model is examined on real data from the information technology industry, under-utilized temperature control units are identified, and system-wide predictions are generated under that component's removal. A Bayesian semi-parametric predictive model for unobserved non-linear dose-responses is proposed. The performance is examined on real data from the pharmaceutical industry and the model proves to be capable of identifying dose-response or lack thereof.