Graphical models for multivariate spatial data Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/sn00b1728

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  • In this thesis we focus on a graphical model for multivariate spatially correlated data--isomorphic chain graphs (ICG; Gitelman and Herlihy, 2007). We feel ICG allow flexibility for modeling spatial correlation and are intuitively appealing because each model has an associated graph that visually represents a complex multivariate system. We examine three ICG models: one (IsoY) that assumes the residuals follow a Gaussian spatial process with an independent predictor, another (IsoX) assumes that the predictor follows a Gaussian spatial process and the residuals are independent, and a third (IsoXY) that assumes the response and predictor have a joint spatial process. We enumerate the conditional and marginal independencies and the resulting likelihood factorization for each model. We are able to rely on results provided in Andersson et al. (2001) and Gitelman and Herlihy (2007) to formulate statistical models for the three ICG. However, parameterizing these models as valid spatial models is not as straightforward. Thus, in Chapter 2, we verify for IsoX and IsoY that parametrizations using the available valid univariate spatial covariances do not violate the assumptions needed to use the results in Andersson et al. (2001). In Chapter 3, we demonstrate that IsoXY can be parameterized using multivariate spatial covariance functions. Chapters 2 and 3 provide the groundwork for Chapter 4, in which we apply the three models to a stream sulfate dataset. These results raise several questions that we address via simulations, and we consider how an analyst would select among the ICG models. Also, we investigate whether the skewness in the effective range posterior intervals is related to the strength of spatial correlation--similar to the REML results in Irvine et al. (2007)--or whether it can be attributed to fitting an incorrect model. And finally, we explore the consequences of assuming an incorrect ICG on parameter estimation. Our work contributes to the field of spatial statistics by providing an additional way to visually display multivariate spatial models. Also, we present accessible suggestions for how to select among the ICG models. Code is provided such that one can implement these models under the Bayesian paradigm using the available freeware, Winbugs (Lunn et al., 2000).
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  • description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 2007-10-22T17:22:51Z (GMT) No. of bitstreams: 1 Irvine_thesis.pdf: 716548 bytes, checksum: 2016f881f5ed4eddda4d6eaf21cf91fd (MD5)
  • description.provenance : Made available in DSpace on 2007-10-22T17:22:53Z (GMT). No. of bitstreams: 1 Irvine_thesis.pdf: 716548 bytes, checksum: 2016f881f5ed4eddda4d6eaf21cf91fd (MD5)
  • description.provenance : Submitted by Kathryn Irvine (georgitk@onid.orst.edu) on 2007-10-09T21:19:56Z No. of bitstreams: 1 Irvine_thesis.pdf: 716548 bytes, checksum: 2016f881f5ed4eddda4d6eaf21cf91fd (MD5)
  • description.provenance : Approved for entry into archive by Julie Kurtz(julie.kurtz@oregonstate.edu) on 2007-10-10T19:36:16Z (GMT) No. of bitstreams: 1 Irvine_thesis.pdf: 716548 bytes, checksum: 2016f881f5ed4eddda4d6eaf21cf91fd (MD5)

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