Spatio-Temporal Hererogeneity Analysis and Modern Phytometry

今年的提案与2009年的提案是一致的，因为它是建立在目前的发现补助金所取得的成果的基础上，同时包括新的挑战和独特的研究和培训机会。1992年以来，我在植物科学系担任统计学教授的位置多年来一直影响着我的研究兴趣，特别是在2003年麦吉尔大学麦克唐纳校区为农业和环境研究建立CT扫描实验室之后，感谢NSERC和CFI的支持（CT：计算机断层扫描）。我的2009年和2014年提案的两个部分并不是不相交的;第二部分是为了提高所研究的异质性的一些定量和统计方面的“植物科学品味”。 各部分之间计划的研究和培训比例保持2/3（时空异质性分析）和1/3（现代植物测量学）。* 2010-5发现补助金使我能够在多个领域取得实质性进展，这些领域对我未来的研究工作至关重要，研究生，研究专业人员和合作者。我现在打算继续：㈠利用适当和有效的估计和测试程序，丰富必须分析越来越复杂的空间数据集的从业人员的统计资料库; ㈡向空间和时间数据分析统计方法的用户通报这些方法在应用条件和假设方面的利弊;（iii）测量和模拟基本生命过程和灾害性自然现象;（iv）通过结合（i）-（iii），增加对关键问题的知识和理解，以便得出合理的结论并做出相关决定。有4名硕士生，1名博士生。我将（i）补充和完成CRAD系列项目，包括一名学生、一名博士后研究员和一名研究助理（CRAD：Co-Regionalization Analysis with a Drift），（i.1）制定最后一项显著性检验，（i.2）研究放宽各向同性假设的影响，同时向用户提供CRAD-ET软件，（2）阐明了点模式分析中的一些假设，为现有的点过程建模提供了更好的指导，并为点过程建模找到了一条新的途径;（iii）通过低震级事件中地震数据目录不完整的实际问题，探讨加拿大三个地区地震时空分布的建模;（iv）进行一项全面的木材CT扫描项目，在该项目中，将以前所未有的水平对生长年份、方向和树干高度对木材密度的影响进行统计评估;及（v）进行一项植物CT扫描研究，其中多重分形假设将以微型针叶树分枝模式的原始程序进行测试。

This year's proposal is in line with the 2009 one because it is built on the results obtained thanks to the current Discovery Grant, while including new challenges and unique research and training opportunities. My location in a plant science department as statistics professor since Dec. 1992 has influenced my research interests over the years, especially after the creation of the CT Scanning Laboratory for agricultural and environmental research on Macdonald Campus of McGill in 2003, thanks to NSERC and CFI support (CT: computed tomography). The two parts of my 2009 and 2014 proposals are not disjoint; there is a second part to enhance the `plant-science taste' of some quantitative and statistical aspects of the heterogeneity studied. The ratio of planned research and training between the parts remains 2/3 (Spatio-Temporal Heterogeneity Analysis) and 1/3 (Modern Phytometry).*******The 2010-5 Discovery Grant allowed me to make substantial progress in multiple areas of critical importance for my future research work, with graduate students, research professionals and collaborators. I now intend to continue to (i) enrich the statistical library of practitioners who have to deal with the analysis of more and more complicated spatial datasets, with appropriate and performing estimation and testing procedures; (ii) inform the users of statistical methods designed for spatial and temporal data analyses, of the pros and cons of those methods regarding the conditions of application and assumptions; (iii) measure and model fundamental Life processes and disastrous natural phenomena; and (iv) by combining (i)-(iii), increase the knowledge on and understanding of critical issues, so that sound conclusions are drawn and relevant decisions can be made.*******With 4 M.Sc. students, 1 Ph.D. student, 1 post-doctoral fellow, and 1 research associate, I shall (i) complement and finalize the series of CRAD projects (CRAD: Co-Regionalization Analysis with a Drift), by (i.1) developing one last test of significance and (i.2) studying the implications of relaxing the isotropy assumption, while providing users with the software CRAD-ET, which will incorporate all main estimation (E) and testing (T) procedures; (ii) clarify a number of assumptions in point pattern analysis, provide better guidelines for existing point process modeling, and find a new avenue for it; (iii) approach the modeling of the spatio-temporal distribution of earthquakes in three regions of Canada, via the practical problem of incompleteness of an earthquake data catalog in events of lower magnitude; (iv) do a comprehensive Wood CT Scan project, in which the effects of year of growth, direction and height in the stem on wood density will be statistically assessed at an unprecedented level; and (v) conduct a Plant CT Scan study in which the multi-fractal hypothesis will be tested with an original procedure on branching patterns of miniature coniferous trees.