Title: Controlling Sources of Inaccuracy in Stochastic Kriging,
Abstract: Scientists and engineers commonly use simulation models to study real systems
for which actual experimentation is costly, difficult, or impossible. Many
simulations are stochastic in the sense that repeated runs with the same input
configuration will result in different outputs. For expensive or time-consuming
simulations, stochastic kriging \citep{ankenman} is commonly used to generate
predictions for simulation model outputs subject to uncertainty due to both
function approximation and stochastic variation. Here, we develop and justify a
few guidelines for experimental design, which ensure accuracy of stochastic
kriging emulators. We decompose error in stochastic kriging predictions into
nominal, numeric, parameter estimation and parameter estimation numeric
components and provide means to control each in terms of properties of the
underlying experimental design. The design properties implied for each source
of error are weakly conflicting and broad principles are proposed. In brief,
space-filling properties "small fill distance" and "large separation distance"
should balance with replication at distinct input configurations, with number
of replications depending on the relative magnitudes of stochastic and process
variability. Non-stationarity implies higher input density in more active
regions, while regression functions imply a balance with traditional design
properties. A few examples are presented to illustrate the results.