A computer model is a computer code that implements a mathematical model of a physical process. A computer code is often complicated and can involve a large number of inputs, so it may take hours or days to produce a single response. Screening to determine the most active inputs is critical for reducing the number of future code runs required to understand the detailed input-output relationship, since the computer model is typically complex and the exact functional form of the input-output relationship is unknown. This dissertation proposes a new screening method that identifies active inputs in a computer experiment setting. It describes a Bayesian computation of sensitivity indices as screening measures. It provides algorithms for generating desirable designs for successful screening.
The proposed screening method is called GSinCE (Group Screening in Computer Experiments). The GSinCE procedure is based on a two-stage group screening approach, in which groups of inputs are investigated in the first stage and then inputs within only those groups identified as active at the first stage are investigated individually at the second stage. Two-stage designs with desirable properties are constructed to implement the procedure. Sensitivity indices are used to measure the effects of inputs on the response. Inputs with large sensitivity indices are determined by comparison with a benchmark null distribution constructed from user-specified, low-impact inputs. The use of low-impact inputs is useful for screening out inputs having small effects as well as those that are totally inert. Simulated examples show that, compared with one-stage procedures, the GSinCE procedure provides accurate screening while reducing computational effort.
In this dissertation, the sensitivity indices used as screening measures are computed in a Gaussian process model framework. This approach is known to be computationally efficient by using small numbers of expensive computer code runs for the estimation of sensitivity indices. The existing approach for quantitative inputs is extended so that sensitivity indices can be computed when inputs include a qualitative input in addition to quantitative inputs.
An orthogonal design in which the design matrix has uncorrelated columns is important for estimating the effects of inputs. Moreover, a space-filling design for which design points are well spread out is needed to explore the experimental region thoroughly. New algorithms for achieving such orthogonal space-filling designs are proposed in this dissertation. The three kinds of software are provided for the proposed GSinCE procedure, computation of sensitivity indices, and design search algorithms.