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Abstract:
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Youngjo Lee and John Nelder introduced an important body of literature on h-likelihood methods and hierarchical generalized linear models, which expanded the scope of generalized linear regressions with correlated errors and revived an interest in Henderson's pioneering ideas on mixed linear equations and best linear unbiased predictions. In this talk, I shall discuss how their h-likelihood methods pave the way for a deeper understanding of kriging and residual maximum likelihood estimation for various classes of spatial and spatial-temporal models that include conditional and intrinsic auto-regressions, de Wijs and Matern processes, and stochastic partial differential equations such as advection-diffusion. In addition, I shall discuss how h-likelihood methods allow for scalable matrix-free computations, bootstrap sampling and residual analysis. The importance of these developments will be emphasized with applications from environmental science. The talk will conclude with comments about future directions and potential challenges.
Part of this talk is based on collaborations with former PhD students Somak Dutta and Chunxiao Wang. The work is supported by a NSF Career award.
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