Interval metamodels for the analysis of simulation Input–Output relations

• An interval metamodel describes a simulation model input–output relationship.
• A Bayesian approach is proposed to test the interval metamodel goodness of fit.
• It allows to analyze the shape of a simulation model response surface.
• Schelling’s segregation model is used as an example of the application.

We analyze the use of simulation metamodels for understanding the relationship between the inputs and outputs of stochastic simulation models. Such metamodels are expected to have a simple structure, but can be conditionally biased. In order to overcome this limitation, we propose the use of interval metamodels that assume that the prediction of the metamodel is an interval rather than a single point. We develop a Bayesian procedure that allows a researcher to verify how well an interval metamodel covers a response surface of a simulation model. The proposed method is illustrated by application to Schelling’s segregation model. The example shows how the procedure can help a researcher to identify non-obvious characteristics of a simulation model response surface.