Spatio-Temporal Hererogeneity Analysis and Modern Phytometry

今年的提案与2009年的提案是一致的，因为它建立在当前探索基金所取得的成果的基础上，同时包括了新的挑战和独特的研究和培训机会。从1992年12月起，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NSERC和CFI的支持下(CT：计算机断层扫描)在麦吉尔的麦克唐纳校区创建了用于农业和环境研究的CT扫描实验室之后。我的2009年和2014年提案的两个部分并不是不相交的；还有第二个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的比例仍然是2/3(时空异质性分析)和1/3(现代植物测量)。*2010-2005年度的发现补助金使我与研究生、研究专业人员和合作者在对我未来研究工作至关重要的多个领域取得了实质性进展。我现在打算继续：(1)丰富从业者的统计数据库，他们必须处理越来越复杂的空间数据集的分析，并采用适当的估计和测试程序；(2)告知用户为空间和时间数据分析而设计的统计方法，这些方法关于适用条件和假设的利弊；(3)测量基本生命过程和灾难性自然现象并建立模型；和(4)结合(1)-(3)，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。学生，1名博士后，1名博士后和1名研究助理，我将(I)补充和最终确定CRAD系列项目(CRAD：带漂移的协区域化分析)，通过(i.1)开发最后一个重要性检验和(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，该软件将纳入所有主要估计(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)通过较低震级地震数据目录的不完整这一实际问题，对加拿大三个地区地震的时空分布进行建模；(Iv)开展一个综合性的Wood CT扫描项目，对树干生长年份、方向和高度对木材密度的影响进行前所未有的统计评估；(V)进行一项植物CT扫描研究，其中将用关于微型针叶树分枝模式的原始程序来检验多重分形假说。

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.