Revealing the interlevel dependence structure of categorical inputs in numerical environmental simulations with kernel model selection
Abstract
Model uncertainties are generally integrated in environmental long-running numerical simulators via a categorical variable. By focusing on Gaussian process (GP) models, we show how different categorical kernel models (exchangeable, ordinal, group, etc.) can bring valuable insights into the correlation of the simulator output values computed for different levels of the categorical variable, i.e., the interlevel dependence structure. Supported by two real case applications (cyclone-induced waves and reservoir modeling), we have proposed a cross-validation approach to select the most appropriate kernel by finding a trade-off between predictability, explainability, and stability of the covariance coefficients. This approach can be used effectively to support some physical assumptions regarding the categorical variable. Through comparison to tree-based techniques, we show that GP models can be considered a satisfactory compromise when only a few model runs (∼100) are available by presenting a high predictability and a concise and graphical way to map the interlevel dependence structure.