Modeling Nonstationary Processes Through Dimension Expansion

Luke Bornn, Gavin Shaddick and James V. Zidek

Journal of the American Statistical Association, 2012, vol. 107, issue 497, 281-289

Abstract: 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.

Date: 2012
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DOI: 10.1080/01621459.2011.646919

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