Modeling Nonstationary Processes Through Dimension Expansion

By Luke Bornn, Gavin Shaddick, James V. Zidek. 2010

109 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Environmental Engineering, Statistics and Probability

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Citations in the corpus

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, background): “There are many other examples of nonstationary covariance functions [3], [22], [54], [70], [118], [121], [126], [132] that have been proposed for GP regression along with closely related output warping techniques [141] that can also model certain kinds of nonstationary processes.”
Second-order non-stationary modeling approaches for univariate geostatistical data (2017, methodology): “Bornn et al. (2012) propose a method consisting of embedding the study region in a higher dimensional space to recover the stationarity of the random function.”
Non-Stationary Dependence Structures for Spatial Extremes (2014, background): “Alternatively,Sampson and Guttorp(1992),Perrin and Monestiez(1999),Schmidt and O’Hagan(2003) andAnderes and Stein(2008) created nonstationary processes by smooth deformations of isotropic random elds.Bornn et al. (2012) proposed modeling non-stationarity through dimension expansion.Lindgren et al. (”
Spatial models with explanatory variables in the dependence structure (2014, background): “This approach has been further developed in Schmidt and O’Hagan (2003); Schmidt et al. (2011); Bornn et al. (2012).”
Heteroscedastic Treed Bayesian Optimisation (2014, background): “A latent space representation in higher dimensions was also proposed by Bornn et al. (2012).”