A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods

The effects of temperature on the Ethiopian Bush-crow and the White-tailed Swallow

Understanding the factors which determine the distributions of species is challenging. In response to recent anthropogenic climate change species’ ranges are already changing, adding to the complexity of describing their ecological boundaries. The threat posed to species by climate change cannot be understated, and our ability to understand the drivers and mechanisms which underlie species’ responses is critical to our strategies to conserve them. The Ethiopian Bush-crow’s Zavattariornis stresemanni distribution was recently described by an envelope of cooler, drier climate than the surrounding area. This finding raised an intriguing possibility; could this abundant, generalist and charismatic species be limited to a tiny corner of the world by its response to climatic variables alone? That the White-tailed Swallow Hirundo megaensis occurs in a near identical area only adds to this curiosity; how can two unrelated species be globally restricted to the same small area? I address the following questions. What are the effects of temperature on the distribution and local density of the Ethiopian Bush-crow and White-tailed Swallow? How is Bush-crow behaviour affected by temperature? What are the effects of temperature on the breeding success of the White-tailed Swallow? What are the consequences of climatic range-restriction for the conservation of the two species? I found that both species’ ranges are neatly described by distribution models, in which the most important variable was maximum temperature of the warmest month. Bush- crow local density declines as temperatures rise, and their foraging behaviour is negatively impacted by high temperatures, compared to two sympatric starling species. The White-tailed Swallow shows similar negative trends in abundance, and displays a reduction in breeding success as ambient temperatures increase during its breeding season. In both cases, wider-ranging sympatric species do not show the same negative responses to temperature. Both the Ethiopian Bush-crow and White-tailed Swallow are projected to lose a significant proportion of their range over the coming century, raising the level of conservation concern for the species.I was generously funded by the Natural Environment Research Council (NERC) through a CASE partnership with the Royal Society for the Protection of Birds (RSPB), with additional support from the British Birdfair, the African Bird Club, the British Ornithologists Union, the University of Cambridge, the Tim Whitmore Zoology Fund, the Cambridge Philosophical Society, Worts Travelling Scholars Fund, Magdalene Graduate Tutor’s and vacation study grants, and Sir Colin Corness. All fieldwork contained within this thesis was carried out under research permits obtained from the Ethiopian Wildlife Conservation Authority