Statistical methods for longitudinal and censored or missing data

在自然资源管理中，决策越来越多地基于对复杂数据库的分析。这种复杂性可能源于数据库的地理和/或空间性质(例如，关于佩戴GPS设备的动物访问的几个日常位置的信息)或其纵向性质(例如，现在普遍的做法是在同一实验单位上进行多次测量，无论是动物、鱼类种群还是气象站)。 许多这种情况的共同困难是，数据库中的某些信息片段缺失或不完整，和/或模型的元素在数据中没有直接观察到。例如，在测量树木的生长时，如果一棵树在最后一次测量时死亡，但在倒数第二次测量时仍然活着，那么这棵树的确切死亡时间并不确切，而只是位于最后两次测量定义的时间间隔内；这种不完整的信息被称为“区间审查”。或者，当模拟野牛如何选择它们的栖息地时，每种动物的“口味”被明确地包括在统计模型中，但数据库中没有对这些“口味”的直接测量。 这一研究方案的主要目标是开发和改进在某些观测数据被审查、遗漏或未被观测时分析纵向数据的模型和方法，特别侧重于自然资源管理中使用的方法。使用统计方法处理缺失数据，我们将提出新的模型和方法，用于纵向和生存数据的联合建模(例如，树木生长建模)，用于使用潜在状态空间过程的纵向数据的建模(例如，商业鱼类种群建模)，以及用于资源选择函数的估计(例如，动物栖息地选择研究)。

In the management of natural resources, decisions are becoming increasingly based on the analysis of complex databases. This complexity may arise from the geographic and/or spatial nature of the database (e.g., information on several daily locations visited by animals wearing GPS devices) or from its longitudinal nature (e.g., it is now common practice to take multiple measurements on a same experimental unit, be it an animal, a fish population, a weather station). A difficulty that is common to many such situations is the fact that some pieces of information are missing or incomplete in the database and/or elements of the models are not directly observed in the data. For instance when measuring the growth of trees, if a tree is dead at the time of the last measurement but was alive at the second to last measurement, then the exact time of death of this tree is not known exactly, but only to lie in the time interval defined by the last two measurements; such incomplete information is known as "interval censoring". Or when modeling how bison select their habitat, the "tastes" of each animal are explicitly included as elements of the statistical model, but no direct measurements of these "tastes" are part of the database. The main objective of this research program is to develop and improve models and methods for the analysis of longitudinal data when some observations are censored, missing or unobserved, with a particular focus on the methods used in the management of natural resources. Using statistical methods to handle missing data, we will propose new models and methods for the joint modeling of longitudinal and survival data (e.g., tree growth modeling), for the modeling of longitudinal data using latent state space processes (e.g., commercial fish stock modeling) and for the estimation of resource selection functions (e.g., animal habitat selection studies).