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A Reparametrization Approach for Dynamic Space-Time Models

  • Hyeyoung Lee
  • Sujit K. Ghosh
Article

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.

AMS Subject Classification

62H11 62F15 65C60 

Keywords

Computational efficiency Dynamic models Reparametrization Spatial models 

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Copyright information

© Grace Scientific Publishing 2008

Authors and Affiliations

  1. 1.Korea Institute of Patent InformationSeoulKorea
  2. 2.Department of Statistics at North Carolina N]State UniversityRaleighUSA

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