TY - JOUR TI - Contributions to crossover designs and quantile analysis for computer experiments DO - https://doi.org/doi:10.7282/t3-kvtk-rg65 PY - 2019 AB - This dissertation develops methodologies for optimal crossover designs and quantile modeling in computer experiments. It consists of two parts. The fist part of the dissertation is regarding finding optimal crossover designs for qualitative treatment effect. The second part of the dissertation is to investigate quantile analysis in computer experiments. Crossover designs for quantitative variables are common in practice but the theoretical developments are overlooked in the design literature. Motivated by an experimental design problem in cell biology. new classes of optimal crossover designs are introduced under different model assumptions on carryover effects with quantitative variables. Theoretical properties of optimal designs are derived which are different from their counterparts with qualitative variables. To efficiently construct optimal designs, systematic procedures are proposed based on a collection of swap operations. The proposed optimal designs are demonstrated by simulation studies and an application in cell adhesion experiments. The characteristic of computer experiments are that they are deterministic, time-consuming and involve large number of variables. Due to these features of computer experiments, Gaussian process model is a widely used interpolator as an emulator in computer experiments to model mean structure of response. It is also of interest to model different quantiles. Motivated by finding an analogy to Gaussian process models for quantile analysis in computer experiments, a new Bayesian quantile analysis model for computer experiments is introduced. New model developed could capture the non-linearity and smoothness of underlying quantile functions. Quantile predictions in the new model for observed inputs agree on true quantiles asymptotically. With some constraints, asymptotic consistency of coefficients estimation is derived. There is no issue of quantile curves crossing each other in proposed model for quantile prediction of observed inputs. KW - Carryover effect KW - Statistics and Biostatistics LA - English ER -