Functional Data Analysis, Mixed Models and Hidden Markov Models

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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.