Premium
Nonparametric measures of association between a spatial point process and a random set, with geological applications
Author(s) -
Foxall Rob,
Baddeley Adrian
Publication year - 2002
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/1467-9876.00261
Subject(s) - bivariate analysis , univariate , point process , nonparametric statistics , bivariate data , statistic , multiplicative function , statistics , mathematics , inference , parametric statistics , point (geometry) , spatial analysis , function (biology) , econometrics , computer science , data mining , multivariate statistics , artificial intelligence , geometry , mathematical analysis , evolutionary biology , biology
In mining exploration it is often desired to predict the occurrence of ore deposits given other geological information, such as the locations of faults. More generally it is of interest to measure the spatial association between two spatial patterns observed in the same survey region. Berman developed parametric methods for conditional inference about a point process X given another spatial process Y . This paper proposes an alternative, nonparametric, approach using distance methods, analogous to the use of the summary functions F , G and J for univariate point patterns. Our methods apply to a bivariate spatial process ( X , Y ) consisting of a point process X and a random set Y . In particular we develop a bivariate analogue of the J ‐function of van Lieshout and Baddeley which shows promise as a summary statistic and turns out to be closely related to Berman's analysis. Properties of the bivariate J ‐function include a multiplicative identity under independent superposition, which has no analogue in the univariate case. Two geological examples are investigated.