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1、ModellingMultivariateCountsVaryingContinuouslyinSpace*UniversityPressScholarshipOnlineOxfordScholarshipOnlineBayesianStatistics9JoséM.Bernardo,M.J.Bayarri,JamesO.Berger,A.P.Dawid,DavidHeckerman,AdrianF.M.Smith,andMikeWestPrintpublicationdate:2011PrintISBN-13:9780199694587PublishedtoOxfordScholarshi
2、pOnline:January2012DOI:10.1093/acprof:oso/9780199694587.001.0001ModellingMultivariateCountsVaryingContinuouslyinSpace*AlexandraM.SchmidtMarcoA.RodríguezDOI:10.1093/acprof:oso/9780199694587.003.0020AbstractandKeywordsWediscussmodelsformultivariatecountsobservedatfixedspatiallocationsofaregionofinter
3、est.OurapproachisbasedonacontinuousmixtureofindependentPoissondistributions.Themixingcomponentisabletocapturecorrelationamongcomponentsoftheobservedvectorandacrossspacethroughtheuseofalinearmodelofcoregionalization.Weintroduceheretheuseofcovariatestoallowforpossiblenon‐stationarityofthecovariancest
4、ructureofthemixingcomponent.WeanalysejointspatialvariationofcountsoffourfishspeciesabundantinLakeSaintPierre,Quebec,Canada.Modelsallowingthecovariancestructureofthespatialrandomeffectstodependonacovariate,geodeticlakedepth,showedimprovedfitrelativetostationarymodels.Keywords:AnimalAbundance,Anisotr
5、opy,LinearModelofCoregionalization,Non‐Stationarity,PoissonLog‐NormalDistribution,RandomEffectsPage1of31ModellingMultivariateCountsVaryingContinuouslyinSpace*SummaryWediscussmodelsformultivariatecountsobservedatfixedspatiallocationsofaregionofinterest.Ourapproachisbasedonacontinuousmixtureofindepen
6、dentPoissondistributions.Themixingcomponentisabletocapturecorrelationamongcomponentsoftheobservedvectorandacrossspacethroughtheuseofalinearmodelofcoregionalization.Weintroduceheretheuseofcovariatestoallowforpossiblenon‐stationarityofthecovariancestructureofthemixingcomponent.Weanalysejointspatialva
7、riationofcountsoffourfishspeciesabundantinLakeSaintPierre,Quebec,Canada.Modelsallowingthecovariancestructureofthespatialrandomeffectstodependonacovariate,geodeticlakedepth,showedimprovedfitrelativetostation
