Spatio-Temporal Hererogeneity Analysis and Modern Phytometry

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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.