  In this paper, 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
multi-dimensional scaling, group lasso, and latent variables 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
data set 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.

Methodology;Applications