Modelling and analysis of spatial point patterns

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The focus of my research is the modelling, analysis, and application of spatial (particularly planar) point patterns.  Examples of spatial point patterns include locations of mineral deposits in a region being explored by a mining company, locations of birds' nests in a nesting area, locations of towns in a geographical region, locations of forest fires in a region, and the locations of stars, quasistellar objects, or galaxies in a sector of outer space.The simplest of such patterns exhibit "complete spatial randomness" (CSR).  Other patterns depart from CSR by having trends in their intensity (density or concentration of points) or by having dependence or interaction among the points.  Often the practical questions which arise involve assessing whether trends are associated with possible explanatory variables (covariates) such as terrain characteristics, vegetation, and soil type.  In the case of point patterns of forest fires, covariates also include concentrations of human population and proximity to aspects of human activity such as mills, roads, and railroads.Assessing statistically the evidence for association of trends with covariates requires that the (possible) interaction between points, mentioned above, be allowed for.  This in turn requires modelling such interaction.  My research is focussed on such modelling, assessment of the adequacy of the models, and hence assessment of the influence of covariates upon trends.  The results will be applied to and validated upon patterns of forest fire locations in New Brunswick.