Modelling and analysis of spatial point patterns

我的研究重点是空间（特别是平面）点模式的建模、分析和应用。空间点模式的例子包括矿业公司正在勘探的区域内矿藏的位置、筑巢区域内鸟巢的位置、地理区域内城镇的位置、区域内森林火灾的位置以及外层空间某一区域内恒星、类星体或星系的位置。这种模式中最简单的表现为“完全空间随机性”（CSR）。其他模式通过其强度趋势（点的密度或集中度）或点之间的依赖或相互作用而偏离CSR。通常出现的实际问题涉及评估趋势是否与可能的解释变量（协变量）有关，如地形特征、植被和土壤类型。在森林火灾的点模式的情况下，协变量还包括人口的集中和接近人类活动的方面，如工厂、道路和铁路。对趋势与协变量关联的证据进行统计评估，需要考虑到上述点之间（可能的）相互作用。这反过来又需要对这种相互作用进行建模。我的研究集中在这样的建模，评估模型的充分性，从而评估协变量对趋势的影响。研究结果将应用于新不伦瑞克省森林火灾地点的模式并进行验证。

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.