Modeling Nonstationary Processes Through Dimension Expansion

• Published in: Journal of the American Statistical Association Vol. 107; no. 497; pp. 281 - 289
• Main Authors: Bornn, Luke, Shaddick, Gavin, Zidek, James V
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis Group 01.03.2012; Taylor & Francis Ltd
• Subjects: Air pollution; Correlations; Covariance; data collection; Dimension expansion; Environmental processes; Geodetic position; Modeling; multidimensional scaling; Nonparametric models; Nonstationary modeling; Perceptual localization; Solar radiation; Spatial models; Spatial statistics; Statistical methods; Statistics; Sustainable agriculture; Theory and Methods; United Kingdom; United Kingdom > UK
• ISSN: 1537-274X; 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2011.646919

In this article, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher-dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multidimensional scaling, group lasso, and latent variable models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a comparison with existing methods in a simulated environment, dimension expansion is studied on a classic test-bed dataset historically used to study nonstationary models. Following this, we explore the use of dimension expansion in modeling air pollution in the United Kingdom, a process known to be strongly influenced by rural/urban effects, amongst others, which gives rise to a nonstationary field.