Fast and Effective Statistical Inference for Spatio-Temporal Data, with Applications in Marine Ecology
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Data in marine ecology are often characterized by substantial observation noise, patchiness in sampling coverage, and complex dynamics. Statistical techniques for analyzing these data need to account for complicated data generating mechanisms while still being computationally tractable. In this thesis we develop statistical models (in a maximum likelihood framework) that account for these difficulties to address two important questions in marine ecology: how can we infer an individual animal's behaviour from observing only their movement? how can we use observations of fish presence, counts, and/or abundance from scientific surveys to gain insight into the spatio-temporal dynamics of the fish population? Standard hidden Markov models (HMMs) for inferring behaviour from animal movement paths are shown to perform poorly when the movement includes autocorrelation not accounted for by the HMM framework. We develop an extension of the HMM that can account for this additional autocorrelation and provide diagnostics for determining when the autocorrelation is present. We analyze the movement paths of two grey seals to further validate our new modelling framework. Scientific surveys often use a stratified random sampling design to generate data with good spatial coverage over multiple decades with hundreds of spatially referenced observations per year. These datasets are too large to be analyzed with traditional methods, so we adapt the nearest neighbour Gaussian process, a modern advance in computationally efficient spatial modelling, for use within a hierarchical spatio-temporal generalized linear mixed modelling framework. We analyse two real datasets: Carolina wren counts in the state of Missouri, Haddock survey data obtained on the Scotian Shelf, off Nova Scotia. After developing our spatio-temporal model framework for a univariate response, we investigate how to generalize it to a multivariate response variable. Such data often arises in fisheries surveys wherein fish of different age-classes are counted. Specifically, we introduce a cross-sectional copula for our spatio-temporal nearest neighbour Gaussian process and study the behaviour of the copula and inference procedure through simulations.