Spatio-Temporal Hererogeneity Analysis and Modern Phytometry

今年的提案与2009年的提案一致，因为它是建立在当前“发现基金”获得的成果基础上的，同时包含了新的挑战和独特的研究和培训机会。自1992年12月以来，我在植物科学系担任统计学教授，多年来一直影响着我的研究兴趣，特别是在2003年在麦吉尔大学麦克唐纳校区建立了用于农业和环境研究的CT扫描实验室之后，这得益于NSERC和CFI的支持（CT：计算机断层扫描）。我在2009年和2014年提出的建议并不是互不相干的；第二部分是加强对异质性研究的一些定量和统计方面的“植物科学味道”。计划研究和培训在各部分之间的比例保持在2/3（时空异质性分析）和1/3（现代植物学）。******* 2010-5发现基金让我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，与研究生，研究专业人员和合作者。我现在打算继续(I)丰富从业者的统计库，他们必须处理越来越复杂的空间数据集的分析，并使用适当的和执行的估计和测试程序；（ii）告知使用者为空间和时间数据分析而设计的统计方法，以及这些方法在应用条件和假设方面的优缺点；测量和模拟基本生命过程和灾难性自然现象；（iv）结合(i)和（iii），增加对关键问题的认识和理解，从而得出合理的结论并作出相关决定。*******与4名硕士研究生，1名博士研究生，1名博士后研究员和1名研究助理，我将(I)补充并完成一系列CRAD项目（CRAD：共区化分析与漂移），通过（I .1）开发最后一个显著性测试和（I .2）研究放宽各向同性假设的影响，同时向用户提供软件CRAD- et，它将包含所有主要的估计(E)和测试(T)程序；（ii）澄清点模式分析中的一些假设，为现有的点过程建模提供更好的指导，并为其找到新的途径；（iii）通过低震级地震数据目录不完整的实际问题，对加拿大三个地区地震的时空分布进行建模；（iv）进行全面的木材CT扫描项目，在该项目中，生长年份、方向和茎高对木材密度的影响将在前所未有的水平上进行统计评估；(v)进行植物CT扫描研究，其中多重分形假设将用原始程序对微型针叶树的分支模式进行测试。

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.