Advanced Spatial Statistics for Analysing and Visualizing Geo-Referenced Data

Abstract Spatial statistics supplies advanced methods for analysing environmental data, and copes with observational interdependencies similar to the way principal components analysis treats multicollinearity. The U.S. Environmental Protection Agency’s Environmental Monitoring and Assessment Program (EMAP) utilizes kriging from geostatistics for mapping and visualizing environmental data. A conceptual framework is articulated between the interpolation problem in kriging and the missing data problem in spatial statistics, with special reference to relations between the exponential semi-variogram and the conditional autoregressive models. Supercomputing experiments are summarized that simplify numerically the probability density function normalizing factor, which is of particular relevance to estimation tasks for the EMAP project.

[1]  Daniel A. Griffith,et al.  Advanced Spatial Statistics , 1988 .

[2]  Daniel A. Griffith.  Urban Dominance, Spatial Structure, and Spatial Dynamics: Some Theoretical Conjectures and Empirical Implications , 1979 .

[3]  Andries S. Brandsma,et al.  A Biparametric Approach to Spatial Autocorrelation , 1979 .

[4]  R. J. Martin.  Exact maximum likelihood for incomplete data from a correlated gaussian process , 1984 .

[5]  R. Haining,et al.  Maximum likelihood estimation with missing spatial data and with an application to remotely sensed data , 1989 .

[6]  R. Haining.  Spatial Data Analysis in the Social and Environmental Sciences , 1990 .

[7]  J. Besag.  Statistical Analysis of Non-Lattice Data , 1975 .

[8]  Julian Besag,et al.  On a System of Two-dimensional Recurrence Equations , 1981 .

[9]  K. Ord.  Estimation Methods for Models of Spatial Interaction , 1975 .

[10]  Daniel A. Griffith,et al.  SUPERCOMPUTING AND SPATIAL STATISTICS: A RECONNAISSANCE* , 1990 .

[11]  M. Bartlett.  The statistical analysis of spatial pattern , 1974, Advances in Applied Probability.

[12]  Peter R. King,et al.  Generation of correlated properties in heterogeneous porous media , 1988 .

[13]  Daniel A. Griffith,et al.  A STATISTICAL APPROACH TO THE PROBLEM OF MISSING SPATIAL DATA USING A FIRST‐ORDER MARKOV MODEL , 1984 .

[14]  T. Coburn.  Spatial Data Analysis by Example , 1991 .

[15]  B. Ripley.  Statistical inference for spatial processes , 1990 .

[16]  D A Griffith,et al.  Statistical Analysis of Spatial Data in the Presence of Missing Observations: A Methodological Guide and an Application to Urban Census Data , 1989, Environment & planning A.

[17]  Daniel A. Griffith,et al.  Simplifying the normalizing factor in spatial autoregressions for irregular lattices , 1992 .

[18]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .