Expanded Multivariate Adaptive Regression Splines for Emulating Computational Models

• Activity Number: 91
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 9:30 PM to 10:15 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Naveen Narisetty* and Vijay Nair and Ji Zhu and Zach Zhang
• Companies: University of Michigan and University of Michigan and University of Michigan and University of Michigan
• Keywords: Statistical emulator ; Computational models ; Regression Splines ; Climate models ; Large scale models

Abstract

Computational models are used to study many complex phenomena related to climate, where physical experiments are not feasible. In practice, a statistical model is used to fit the output from limited number of evaluations of the computational model, and the resulting "emulator" is used to approximate the input-output relationship. The most commonly used method for this purpose is Gaussian Spatial Process (GaSP), where the output is viewed as the realization of a Gaussian process. We compare the performance of GaSP with flexible regression-based approaches including multivariate adaptive regression splines (MARS), smoothing-spline anova, multiple additive regression tree model, and a new method we develop: expanded multivariate adaptive regression splines model (EMARS). Our empirical comparisons show that EMARS has better predictive performance than GaSP in a variety of situations. Moreover, it is computationally much more efficient and it can be implemented using the current MARS algorithm. We use EMARS to emulate a large scale climate model to study the relationship of precipitation rate with several input variables of interest.