A Reparametrization Approach for Dynamic Space-Time Models

Abstract

Researchers in diverse areas such as environmental and health sciences are increasingly working with data collected across space and time. The space-time processes that are generally used in practice are often complicated in the sense that the auto-dependence structure across space and time is non-trivial, often non-separable and non-stationary in space and time. Moreover, the dimension of such data sets across both space and time can be very large leading to computational difficulties due to numerical instabilities. Hence, space-time modeling is a challenging task and in particular parameter estimation based on complex models can be problematic due to the curse of dimensionality. We propose a novel reparametrization approach to fit dynamic space-time models which allows the use of a very general form for the spatial covariance function. Our modeling contribution is to present an unconstrained reparametrization method for a covariance function within dynamic space-time models. A major benefit of the proposed unconstrained reparametrization method is that we are able to implement the modeling of a very high dimensional covariance matrix that automatically maintains the positive definiteness constraint. We demonstrate the applicability of our proposed reparametrized dynamic space-time models for a large data set of total nitrate concentrations.

Joint Variable Selection for Fixed and Random Effects in Linear Mixed‐Effects Models

“…As a motivating example, consider a recent study of the association between total nitrate concentration in the atmosphere and a set of measured predictors (Lee and Ghosh, 2008; Ghosh et al, 2010). Nitrate is one of the major components of fine particulate matter across the United States (Malm et al, 2004).…”

Extending Moran's Index for Measuring Spatiotemporal Clustering of Geographic Events

“…These developments paralleled an increasing interest to the analysis of space‐time data in many research fields such as physics, meteorology, economics, and environmental studies. Examples include Deutsch and Pfeifer (, ), Huang and Cressie (), Gelfand et al (), Mardia et al (), Cressie and Huang (), Kyriakidis and Journel (), Wikkle and Cressie (), Stroud, Muller, and Sanso (), Gneiting (), Bertazzon(), Banerjee, Gelfand, and MacEachern (), Banerjee, Gelfand, and Gamerman (), Tonellato (), Di Giacinto (), Huang et al (), Glasbey and Allcroft (), Lee and Ghosh (), Naccarato and Lamberti (), Naccarato (2012). In most cases, measurements of spatiotemporal autocorrelation were results of empirical estimations preformed based on data being analyzed.…”

Inference for mixed models of ANOVA type with high-dimensional data

“…Note that (7) does not depend on the null. Therefore, the difference betweenσ 2 andσ 2 0 can be small under the null whereas it is large under alternatives.…”

“…Modeling the relationship between total nitrate concentration in the atmosphere and a set of measured predictors has received some attention (e.g. [7,1]). Dataset which consists of multiple sites with repeated measurements of pollution and meteorological variables in each site can be obtained from the US EPA Clean Air Status and Trends Network (CASTNet) sites.…”