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Modeling Spatial Covariance Using the Limiting Distribution of Spatio-Temporal Random Walks

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  • Ephraim M. Hanks

Abstract

We present an approach for modeling areal spatial covariance in observed genetic allele data by considering the stationary (limiting) distribution of a spatio-temporal Markov random walk model for gene flow. This stationary distribution corresponds to an intrinsic simultaneous autoregressive (SAR) model for spatial correlation, and provides a principled approach to specifying areal spatial models when a spatio-temporal generating process can be assumed. We apply the approach to a study of spatial genetic variation of trout in a stream network in Connecticut, USA.

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  • Ephraim M. Hanks, 2017. "Modeling Spatial Covariance Using the Limiting Distribution of Spatio-Temporal Random Walks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 497-507, April.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:518:p:497-507
    DOI: 10.1080/01621459.2016.1224714
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    References listed on IDEAS

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    1. Alexandra M. Schmidt & Anthony O'Hagan, 2003. "Bayesian inference for non‐stationary spatial covariance structure via spatial deformations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 743-758, August.
    2. Håvard Rue, 2001. "Fast sampling of Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 325-338.
    3. Ephraim M. Hanks & Mevin B. Hooten, 2013. "Circuit Theory and Model-Based Inference for Landscape Connectivity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 22-33, March.
    4. Hodges, James S. & Reich, Brian J., 2010. "Adding Spatially-Correlated Errors Can Mess Up the Fixed Effect You Love," The American Statistician, American Statistical Association, vol. 64(4), pages 325-334.
    5. Christopher Wikle & Mevin Hooten, 2010. "Rejoinder on: A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 466-468, November.
    6. Kurtz, Thomas G., 1978. "Strong approximation theorems for density dependent Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 223-240, February.
    7. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    8. Ephraim M. Hanks & Erin M. Schliep & Mevin B. Hooten & Jennifer A. Hoeting, 2015. "Restricted spatial regression in practice: geostatistical models, confounding, and robustness under model misspecification," Environmetrics, John Wiley & Sons, Ltd., vol. 26(4), pages 243-254, June.
    9. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    10. Christopher Wikle & Mevin Hooten, 2010. "A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 417-451, November.
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    Cited by:

    1. Wilson J. Wright & Peter N. Neitlich & Alyssa E. Shiel & Mevin B. Hooten, 2022. "Mechanistic spatial models for heavy metal pollution," Environmetrics, John Wiley & Sons, Ltd., vol. 33(8), December.
    2. Sahar Zarmehri & Ephraim M. Hanks & Lin Lin, 2021. "A Sample Covariance-Based Approach For Spatial Binary Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(2), pages 220-249, June.

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