Modeling non-stationary processes through dimension expansion

Luke Bornn, Gavin Shaddick, James V Zidek

Research output: Contribution to journal › Article

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Abstract

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 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 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.
LanguageEnglish
Pages281-289
Number of pages9
JournalJournal of the American Statistical Association
Volume107
Issue number497
DOIs
StatusPublished - Mar 2012

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Nonstationary Processes
Modeling
Latent Variable Models
Lasso
Air Pollution
Stationarity
Testbed
High-dimensional
Projection
Scaling
Nonstationary processes

Cite this

Modeling non-stationary processes through dimension expansion. / Bornn, Luke; Shaddick, Gavin; Zidek, James V.

In: Journal of the American Statistical Association, Vol. 107, No. 497, 03.2012, p. 281-289.

Research output: Contribution to journal › Article

Bornn, L, Shaddick, G & Zidek, JV 2012, 'Modeling non-stationary processes through dimension expansion' Journal of the American Statistical Association, vol. 107, no. 497, pp. 281-289. DOI: 10.1080/01621459.2011.646919
Bornn L, Shaddick G, Zidek JV. Modeling non-stationary processes through dimension expansion. Journal of the American Statistical Association. 2012 Mar;107(497):281-289. Available from, DOI: 10.1080/01621459.2011.646919
Bornn, Luke ; Shaddick, Gavin ; Zidek, James V. / Modeling non-stationary processes through dimension expansion. In: Journal of the American Statistical Association. 2012 ; Vol. 107, No. 497. pp. 281-289
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