Spatio-temporal kriging based on the product-sum model: some computational aspects

The Tensor‐based Feature Analysis of Spatiotemporal Field Data With Heterogeneity

“…They can be roughly divided into the geostatistics analysis and statistical regression-based method (Huysmans et al, 2014). In geostatistics analysis, such as the Kriging (Kleijnen, 2009), generalized Kriging (Xu & Shu, 2015), Bayesian Maximum Entropy (Yu & Wang, 2013), etc., the spatiotemporal heterogeneous variation is considered where the temporal variation is a function of time distance and the spatial variation is a function of spatial distance, and the covariance function is used to describe the structure of heterogeneity (de Marsily et al, 2005). However, for the spatiotemporal heterogeneity, the construction of spatiotemporal covariance often faces problems, such as the inconsistent dimensions of space and time (or the unity of "distance" units of time and space) (Kleijnen, 2009;Xu & Shu, 2015).…”

“…In geostatistics analysis, such as the Kriging (Kleijnen, 2009), generalized Kriging (Xu & Shu, 2015), Bayesian Maximum Entropy (Yu & Wang, 2013), etc., the spatiotemporal heterogeneous variation is considered where the temporal variation is a function of time distance and the spatial variation is a function of spatial distance, and the covariance function is used to describe the structure of heterogeneity (de Marsily et al, 2005). However, for the spatiotemporal heterogeneity, the construction of spatiotemporal covariance often faces problems, such as the inconsistent dimensions of space and time (or the unity of "distance" units of time and space) (Kleijnen, 2009;Xu & Shu, 2015). Although, some spatiotemporal covariance models, such as the separable model (Graeler et al, 2016), nonseparable model (Ruiz-Medina et al, 2016), and product-sum model (De Iaco et al, 2001), are proposed to try to solve the above problems.…”

Evaluation of Groundwater Levels in the Arapahoe Aquifer Using Spatiotemporal Regression Kriging

“…Despite the limited applications to groundwater, spatiotemporal kriging is common to a number of other environmental studies. These studies include the analysis and mapping of precipitation (Martínez et al, ); MODIS temperature and precipitation (Hengl et al, ; Hu et al, ); soil moisture, temperature, and electrical conductivity (Gasch et al, ; Wang et al, ); satellite‐observed CO 2 (Tadic et al, ; Tadić et al, ; Zeng et al, ); ozone data (Xu & Shu, ); NO 2 pollutants (Beauchamp et al, ; De Iaco & Posa, ); standardized precipitation index (Bayat et al, ); gamma dose rates (Heuvelink & Griffith, ); solar irradiance forecasting (Aryaputera et al, ); and soil heavy metal distribution (Yang et al, ).…”

Modelos lineares generalizados espaciais mistos aplicados em estudos de insetos

“…Seja um processo espaço-temporal gaussiano Z definido sobre um domínio espacial S e domínio temporal T , {Z(s, t) : (s, t) ∈ (S × T }, em que S ⊆ ℜ d e T ⊆ ℜ, um processo espaço-temporal estatístico, observações são modeladas como uma realização parcial de uma função aleatória espaço-temporal. (Xu e Shu, 2015). A variação espaço-temporal de Z pode ser decomposta pelos componentes da tendência m(s, t) e de um resíduo estocástico ε(s, t) (Yang et al, 2015), ou seja Z(s, t) = m(s, t) + ε(s, t).…”

“…Para o ajuste de um modelo teórico ao variograma empírico apresentado em 3.4 foi utilizado o modelo produto-soma generalizado (Pebesma e Heuvelink, 2016). O variograma, metade da diferença da variância, é geralmente mais útil do que a função de covariância por causa de suas suposições mais fracas (Xu e Shu, 2015). Assim, temos a relação de covariância e semivariograma em processos estacionários de segunda ordem (média constante e função de covariância estacionária) dado por…”