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、联结模型和捕获-再捕获实验。它提出承担理论调查，并实际实施，新的统计模型，以应对现代挑战的数据分析。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征。为了更好地利用这些数据，将开发统计模型进行分析。在生态学中，现在可以同时记录动物的运动和它所处环境的重要特征。该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环境特征方向的影响，例如其巢穴或营养丰富的斑块。在调查中，抽样组合将用于构建新的灵活方法来估计人口的小面积特征。还将研究在捕获-再捕获实验中改进对难以到达的种群大小的估计的方法。

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.