Preprint #96-20
Sampling Designs and Prediction Methods for Spatially
Generated Data
by
Jeremy Aldworth and Noel Cressie
Abstract
A geostatistical model can provide a powerful way of predicting unknown
parts of some spatial phenomenon. The prediction problem is multivariate
in the sense that one wishes to predict at multiple spatial locations.
The research presented in this paper offers compelling evidence that
spatial dependence in the geostatistical model should be exploited for the
purposes of spatial sampling and analysis, where possible. Even when the
observable process is contaminated with measurement error, there is a
straightforward way to filter it out by appropriately modifying the spatial
prediction equations. In this paper, we show that a geostatistical
analysis of a certain class of non-clustered designs, whether simple random,
stratified random, or systematic with a random start, performs extremely
well with respect to design-based optimality criteria. One important
aspect of our study is the prediction of spatial statistics defined over
small areas (called local regions), that are subsets of a global region
over which a network of sampling sites is chosen. Under circumstances where
both local and nonlinear functions of the process at multiple locations
are to be predicted, it is demonstrated that appropriate geostatistical
analyses perform very well, irrespective of the (non-clustered) sampling
design.
Copies of preprints are available from the author upon request. Use
the preprint number (located at the top of the page) and
make the request directly to the author, Iowa State
University,
Department of Statistics, Snedecor Hall, Ames, IA 50011-1210.