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Computationally efficient statistical differential equation modeling using homogenization

Journal of Agricultural, Biological, and Environmental Statistics

By:
, ,
DOI: 10.1007/s13253-013-0147-9

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Abstract

Statistical models using partial differential equations (PDEs) to describe dynamically evolving natural systems are appearing in the scientific literature with some regularity in recent years. Often such studies seek to characterize the dynamics of temporal or spatio-temporal phenomena such as invasive species, consumer-resource interactions, community evolution, and resource selection. Specifically, in the spatial setting, data are often available at varying spatial and temporal scales. Additionally, the necessary numerical integration of a PDE may be computationally infeasible over the spatial support of interest. We present an approach to impose computationally advantageous changes of support in statistical implementations of PDE models and demonstrate its utility through simulation using a form of PDE known as “ecological diffusion.” We also apply a statistical ecological diffusion model to a data set involving the spread of mountain pine beetle (Dendroctonus ponderosae) in Idaho, USA.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Computationally efficient statistical differential equation modeling using homogenization
Series title:
Journal of Agricultural, Biological, and Environmental Statistics
DOI:
10.1007/s13253-013-0147-9
Volume
18
Issue:
3
Year Published:
2013
Language:
English
Publisher:
Springer
Contributing office(s):
Colorado Cooperative Fish and Wildlife Research Unit
Description:
24 p.
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
First page:
405
Last page:
428