Statistique multidimensionnelle

该研究项目涉及统计科学的几个领域，即几何统计，调查抽样，copula建模和捕获-再捕获实验。它建议进行新的统计模型的理论研究和实际实施，以应对数据分析的现代挑战。在生物力学中，通常收集由旋转平移对组成的刚体运动数据来估计人体关节的几何特性。为了更好地利用这些数据，将建立统计模型进行分析。在生态学中，现在可以同时记录动物的运动及其环境的重要特征。本项目将开发多元循环回归模型，以研究动物的运动方向如何受到其栖息地特征方向的影响，例如其巢穴或富含营养的斑块。在调查中，抽样Copula将被用来构建新的灵活的方法来估计人口的小区域特征。还将研究在捕获-再捕获实验中改进难以到达种群规模估计的方法。

This research project is concerned with several areas of the statistical sciences, namely geometric statistics, survey sampling, copula modeling and capture-recapture experiments. It proposes to undertake the theoretical investigation, and the practical implementation, of new statistical models in response to modern challenges in data analysis. In biomechanics, rigid body motion data, consisting of rotation translation pairs are routinely collected to estimate the geometric characteristics of human joints. To make a better use of these data, statistical models will be developed for their analysis. In ecology it is now possible to record simultaneously the movement of an animal, and important features of its environment. This project will develop multivariate circular regression models to investigate how the direction of movement of an animal is influenced by the direction of features of its environement, such as its den or a patch rich in nutriment. In survey sampling copulas will be used to construct new flexible methods for estimating small area characteristics of a population. Methods for improving the estimation of the size of hard to reach populations in a capture-recapture experiment will also be investigated.