Modeling nonstationary processes through dimension expansion

Reference:

Bornn, L., Shaddick, G. and Zidek, J. V., 2012. Modeling nonstationary processes through dimension expansion. Journal of the American Statistical Association, 107 (497), pp. 281-289.

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Official URL:

http://dx.doi.org/10.1080/01621459.2011.646919

Abstract

In this article, we propose a novel approach to modeling nonstationary spatial fields. The proposed methodworks 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.

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