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Untitled - UFRJ

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Bayesian Computing with INLAHåvard RueDepartment of Mathematical Sciences,Norwegian University of Science and Technology, NorwayMany models in statistics can now to analysed using quick-to-compute integrated nested Laplaceapproximations (INLA) instead tedious MCMC sampling. In this talk I will present the main ideas ofthis approach, which models it can deal with and demonstrate how the analysis can be done in practicefrom within R. The software is available from www.r-inla.org.Bridging the gap between Gaussian fields and Gaussian Markov random fields using stochastic partialdifferential equationsGaussian fields (GFs) and Gaussian Markov random fields (GMRFs) specify both multivariate Gaussiandistributions, but are still very different in the way the distribution is specified. GMRFs are naturallyspecified using full conditionals (with the consequence that marginal properties are transparentin the parametrisation) and has very good computational properties, whereas GFs are specified usingcovariance-functions but has less appealing computational properties. In this talk, I will discuss how tobridge GFs and GMRFs, using stochastic partial differential equations which allow us to go seamlesslybetween the GF and GMRF representation and exploit the best properties of both GFs and GMRFs.The consequence of these results is wide-ranging.22

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