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Most of my work is with ecological data, both developing method to fit ecological models to the data, and analysing the data. We generally used Bayesian approaches, with extensions of GLMs and mixed models.
Spatial and spatio-temporal models of species distributions We have been developing methods to integrate different data sets into a single model of a species' distribution. We want to extend these to model changes in space and time, and then apply them to different species, so we can learn how species respond to climate and land use change, and also how well the models work. This work can focus either on model development or applications of data science and fitting models to learn about how real species behave.
Modelling traits as point processes: Some ecologists are interested in how the distributions of traits change (e.g. do birds become bigger at higher altitudes). If the traits are continuous then we can model them as a point process in trait space (>2D), and use point process machinery to look at how the distributions vary. With good enough data, we can even look to see if species exclude each other, using models for repulsion between points to see if this happens. This project will develop and test these ideas.
Model Selection in GLLVMs: GLLVMs are extensions of GLMs for large multivariate data. We have been developing these methods, but one problem that needs more work is finding out how to compare and select different models. This project would compare several methods that have been developed to see which work well (e.g. in hypothesis tests will reject the null hypothesis 5% of the time when it is true), and could also go on to develop better methods.