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Computationally Efficient Statistical Differential Equation Modeling Using Homogenization

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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.

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Authors and Affiliations

  1. U.S. Geological Survey, Colorado Cooperative Fish and Wildlife Research Unit, Department of Fish, Wildlife, and Conservation Biology, Department of Statistics, Colorado State University, Fort Collins, CO, USA

    Mevin B. Hooten

  2. Department of Mathematics and Computer Science, South Dakota School of Mines and Technology, Rapid City, SD, USA

    Martha J. Garlick

  3. Department of Mathematics and Statistics, Utah State University, Logan, UT, USA

    James A. Powell

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  1. Mevin B. Hooten
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  2. Martha J. Garlick
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  3. James A. Powell
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Correspondence to Mevin B. Hooten.

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Hooten, M.B., Garlick, M.J. & Powell, J.A. Computationally Efficient Statistical Differential Equation Modeling Using Homogenization. JABES 18, 405–428 (2013). https://doi.org/10.1007/s13253-013-0147-9

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