Local Likelihood Estimation for Nonstationary Covariance Functions with Applications to Climate Model Emulation

• Activity Number: 665 - Spatial Methods for Weather, Climate, and Health
• Type: Contributed
• Date/Time: Thursday, August 3, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Yuxiao Li* and Ying Sun
• Companies: King Abdullah University of Science and Technology and King Abdullah University of Science and Technology
• Keywords: Climate Model Emulation ; Local Likelihood ; Nonstationary Modeling ; Parallel Computing

Abstract

In many climate and environmental applications, spatial processes exhibit nonstationarity. Convolution-based approaches are often used to construct nonstationary covariance functions in a Gaussian process for spatial modeling. Although convolution-based models are highly flexible, they are not easy to fit even for datasets of moderate size, and the computation becomes extremely expensive for large datasets. Most existing efficient methods rely on fitting an anisotropic but stationary model locally and reconstruct the spatially-varying parameters. In this paper, we propose a new estimation procedure to approximate a class of nonstationary Matern covariance by local polynomial fitting of the covariance parameters. The proposed method allows for efficient estimation of a richer class of nonstationarity with the locally stationary model as a special case. We also implement algorithms for fast simulations using parallel computing with applications to climate model emulation.