Simplifying Objective Functions and Avoiding Stochastic Search Algorithms in Spatial Sampling Design

• Activity Number: 183
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Gunter Spöck*+ and Jürgen Pilz and Zhengyuan Zhu
• Companies: University Klagenfurt and University Klagenfurt and Iowa State University
• Keywords: spatial sampling design ; design criteria ; deterministic design algorithm ; Karhunen-Loeve expansion ; polar spectral representation

Abstract

Spatial sampling design is concerned with the optimal allocation of samples to spatial coordinates in order to improve the estimation and prediction of spatial random fields. Unfortunately most of the interesting objective functions are so complicated that stochastic search algorithms have to be used to get these design criteria optimized. Our intention is to show that some design criteria show mathematically tractable structure when considering the random field as a linear regression model with infinitely many random coefficients. Either the Karhunen-Loeve expansion or the polar spectral representation may be used to get such a favourable representation. As a special case a design criterion is investigated in more detail taking into account both covariance uncertainty and prediction accuracy, and we provide a deterministic design algorithm to search for the optimal design.