Functional Data Analysis, Mixed Models and Hidden Markov Models

技术进步导致了大量数据的收集，往往具有复杂的结构。因此，数据用户和数学科学家面临着许多数据分析的挑战。我将开发统计方法从这些数据中提取意义。虽然我的方法适用于很多领域，例如研究fitbit数据或推断消费者的购买行为，但我将专注于一个领域的数据，即动物运动。生态学家现在可以在动物身上安装跟踪设备，并可以收集大量的位置数据和与精细运动有关的数据。从这些数据中，生态学家可以更好地了解个体行为，从而更好地了解动物如何利用环境和获取所需资源。我将使用隐马尔可夫模型对动物的行为进行建模，其中动物的行为可以处于几种模式中的一种，例如睡觉或觅食。这些模式不是直接可见的——它们确实是隐藏的。它们是通过特殊的统计技术从动物的运动数据中推断出来的。对于这些类型的数据，我将开发灵活的方法，称为非参数方法。我还将考虑如何收集数据：跟踪设备价格昂贵，电池时间有限，出于道德原因，生态学家可以安装的设备数量和类型受到限制。因此，仔细规划数据收集至关重要。我还将考虑结合步骤选择分析和资源选择函数模型的统计基础。这些技术根据行进的距离、方向和可用的资源来模拟动物的步骤——即位置增量。这类模型的部分分析包括从动物没有去过的地方取样和收集数据。我将为这部分的数据收集开发一个框架。

Technological advances have led to the collection of large amounts of data, often with complex structure.  Thus, data users and mathematical scientists face many data analysis challenges.  I will develop statistical methods to extract meaning from these data.  While my methods will be applicable in many areas, for instance, in studying fitbit data or inferring consumer buying behaviour, I will focus on data from one area, namely from animal movement.  Ecologists can now attach tracking devices to animals and can collect huge amounts of location data and data pertaining to fine-scale movement.  From these data, ecologists can better understand individual behaviour and thus better understand how animals use their environment and access needed resources.  I will model an animal's behaviour using a Hidden Markov Model, where the animal's behaviour can be in one of several modes, such as sleeping or foraging.  These modes are not directly seen - they are indeed hidden.  They are inferred from the animal's movement data via special statistical techniques.   I will develop flexible methods, called nonparametric methods, for these types of data.  I will also consider how data should be collected:  tracking devices are expensive and have limited battery time and, for ethical reasons, ecologists are restricted in the number and type of device that they can attach. So careful planning of data collection is crucial. I will also consider the statistical underpinnings of combined step selection analysis and resource selection function models.  These techniques model an animal's steps -- that is, location increments --  in terms of distance travelled, direction and available resources. Part of the analysis of this type of model involves sampling and collecting data from locations that the animal did not visit. I will develop a framework for this part of the data collection.