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Abstract:
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The Gaussian stochastic process is commonly used for modeling time series and geostatistical data. The Gaussianity assumption, however, is known to be insufficient or inappropriate in many spatial risk assessment settings. In this talk, I discuss the development of specific non-Gaussian models to capture the asymmetry and heavy tails of many real-world datasets indexed in space and time. Introducing a general framework for constructing non-Gaussian spatial processes using transformations of a latent multivariate Gaussian process, we develop a heteroscedastic asymmetric spatial process (HASP) for capturing the non-Gaussian features of environmental or climatic data, such as the heavy tails and skewness. The conditions for this non-Gaussian spatial process to be well defined is discussed at length. The properties of the HASP, especially its marginal moments and covariance structure, are established along with a Markov chain Monte Carlo (MCMC) procedure for sampling from the posterior distribution. The HASP model is applied to the study of a US nitrogen dioxide concentration dataset.
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