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      Gaussian Random Functional Dynamic Spatio-Temporal Modeling of Discrete Time Spatial Time Series Data

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          Abstract

          Discrete time spatial time series data arise routinely in meteorological and environmental studies. Inference and prediction associated with them are mostly carried out using any of the several variants of the linear state space model that are collectively called linear dynamic spatio-temporal models (LDSTMs). However, real world environmental processes are highly complex and are seldom representable by models with such simple linear structure. Hence, nonlinear dynamic spatio-temporal models (NLDSTMs) based on the idea of nonlinear observational and evolutionary equation have been proposed as an alternative. However, in that case, the caveat lies in selecting the specific form of nonlinearity from a large class of potentially appropriate nonlinear functions. Moreover, modeling by NLDSTMs requires precise knowledge about the dynamics underlying the data. In this article, we address this problem by introducing the Gaussian random functional dynamic spatio-temporal model (GRFDSTM). Unlike the LDSTMs or NLDSTMs, in GRFDSTM both the functions governing the observational and evolutionary equations are composed of Gaussian random functions. We exhibit many interesting theoretical properties of the GRFDSTM and demonstrate how model fitting and prediction can be carried out coherently in a Bayesian framework. We also conduct an extensive simulation study and apply our model to a real, SO2 pollution data over Europe. The results are highly encouraging.

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          Most cited references37

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          The use of the multi-model ensemble in probabilistic climate projections.

          Recent coordinated efforts, in which numerous climate models have been run for a common set of experiments, have produced large datasets of projections of future climate for various scenarios. Those multi-model ensembles sample initial condition, parameter as well as structural uncertainties in the model design, and they have prompted a variety of approaches to quantify uncertainty in future climate in a probabilistic way. This paper outlines the motivation for using multi-model ensembles, reviews the methodologies published so far and compares their results for regional temperature projections. The challenges in interpreting multi-model results, caused by the lack of verification of climate projections, the problem of model dependence, bias and tuning as well as the difficulty in making sense of an 'ensemble of opportunity', are discussed in detail.
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            Model choice: a minimum posterior predictive loss approach

            A. Gelfand (1998)
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              Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets

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                Author and article information

                Journal
                2014-05-26
                2016-10-25
                Article
                1405.6531
                087f7a43-d137-4622-b7df-43e1de614a78

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Article length 47 pages excluding reference. Total 27 figures
                stat.ME math.ST stat.TH

                Methodology,Statistics theory
                Methodology, Statistics theory

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