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Hierarchical models and shrinkage estimators

Rankin, Robert (2017) Hierarchical models and shrinkage estimators. PhD thesis, Murdoch University.

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Capture-Mark-Recapture (CMR) models are a large class of hierarchical time-series models for estimating the abundance and survival of individually marked animals. Due to the complex multi-parameter nature of CMR models, CMR practitioners have been enthusiastic adopters of multi-model inference (MMI) techniques. By MMI, I refer loosely to a variety of techniques such as model-selection, model-averaging, Frequentist shrinkage estimators, and Hierarchical Bayesian random-e_ects. In this thesis, I develop and compare methods of MMI in CMR, with application to the movement and abundance of bottlenose dolphins, Tursiops sp., in Australia. I use novel ideas from the _eld of machine learning, as well as revisit old estimation problems like the Marginal Likelihood. As this thesis will show, there are many practical problems to the popular AIC/BIC-based methods in odontocetes CMR studies, such as singularities and boundary-value estimates. This is especially the case when there is a lot of demographic and/or temporal variation. Understanding such heterogeneity is important for conservation and ecological theory, such as the role of individual heterogeneity for estimating abundance (Chapter 3), or sex/age di_erences in movement patterns (Chapter 4). Such heterogeneity can also lead to severe non-identiability problems. I suggest practical solutions through HB models and shrinkage estimators. Chapter 2 reviews MMI theory and presents a new boosting algorithm for the Cormack-Jolly-Seber model. Chapter 3 presents a Hierarchical Bayesian (HB) version of Pollock's Closed Robust Design (PCRD), with emphasis on shrinkage priors and individual heterogeneity. Chapter 4 reviews Bayesian model selection and introduces a technique to estimate Marginal Likelihoods and Bayes Factors for hidden-Markov models, such as the PCRD. Chapter 5 generalizes the HB PCRD into a Multistate CRD model, with emphasis on shrinkage priors for inference on geographic state-transitions.

Publication Type: Thesis (PhD)
Murdoch Affiliation: School of Veterinary and Life Sciences
Supervisor: Bejder, Lars and Pollock, Ken
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