Testing for Isotropy in Spatial Data, With Two
                         Applications

                         Dale Zimmerman

                       University of Iowa

      

Many applications of spatial statistics require an assessment of whether the
small-scale spatial dependence among observations is isotropic, i.e.
invariant to the relative orientation of data locations.  I consider testing for
isotropy for two kinds of spatial data: geostatistical data and spatial point
patterns.  In the geostatistical case, I consider a frequentist approach based
on the extent to which the sample semivariogram satisfies certain equality
constraints implied by isotropy.   In the spatial point pattern case, I
consider a Bayesian approach implemented by Markov chain Monte Carlo
sampling.  The approaches are illustrated using data from an acid
precipitation monitoring network and data on tree locations in a forest.