Bias correction and change measurement in spatio-temporal data

Abstract

A simplistic view of a dataset is that it is collection of numbers. In fact data are much more than that and all data are collected at a set place and time. Often either the location, or the time, is fixed within the dataset and one or both are disregarded. When the place and time of the collection are incorporated into the analysis, the result is a spatio-temporal model. Spatio-temporal data are the focus of this thesis. The majority of the datasets used are radio tracking studies of animals where the objective is to measure the habitat use. Observations are made over a long period of time and a large area. The largest dataset analysed tracks over a hundred animals, in an area larger than 40 square miles, for multiple years. In this context understanding the spatio-temporal relationships between observations is essential. Even data that do not have an obvious spatial component can benefit from spatio-temporal analysis. For example, the data presented on volatility in the stock market do not have an obvious spatial component. The spatial component is the location in the market, not a physical location. Two different methods for measuring and correcting bias are presented. One method relies on direct modelling of the underlying process being observed. The underlying process is animal movement. A model for animal movement is constructed and used to estimate the missing observations that are thought to be the cause of the bias. The second method does not model the animal movement, but instead relies on a Bayesian Hierarchical Model with some simple assumptions. A long running estimation is used to calculate the most likely result without ever directly estimating the underlying equations. In the second section of the thesis two methods for measuring change from shifts in both spatial and temporal location are presented. The methods, Large Diffeomorphic Deformation Metric Mapping (LDDMM) and Diffeomorphic Demons (DD), were originally developed for anatomical data and are adapted here for nonparametric regression surfaces. These are the first applications of LDDMM and DD outside of computational anatomy.