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Bayesian Statistics 9$
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José M. Bernardo, M. J. Bayarri, James O. Berger, A. P. Dawid, David Heckerman, Adrian F. M. Smith, and Mike West

Print publication date: 2011

Print ISBN-13: 9780199694587

Published to Oxford Scholarship Online: January 2012

DOI: 10.1093/acprof:oso/9780199694587.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 13 April 2021

Modelling Multivariate Counts Varying Continuously in Space *

Modelling Multivariate Counts Varying Continuously in Space *

(p.611) Modelling Multivariate Counts Varying Continuously in Space*
Bayesian Statistics 9

Alexandra M. Schmidt

Marco A. Rodríguez

Oxford University Press

We discuss models for multivariate counts observed at fixed spatial locations of a region of interest. Our approach is based on a continuous mixture of independent Poisson distributions. The mixing component is able to capture correlation among components of the observed vector and across space through the use of a linear model of coregionalization. We introduce here the use of covariates to allow for possible non‐stationarity of the covariance structure of the mixing component. We analyse joint spatial variation of counts of four fish species abundant in Lake Saint Pierre, Quebec, Canada. Models allowing the covariance structure of the spatial random effects to depend on a covariate, geodetic lake depth, showed improved fit relative to stationary models.

Keywords:   Animal Abundance, Anisotropy, Linear Model of Coregionalization, Non‐Stationarity, Poisson Log‐Normal Distribution, Random Effects

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