These are some of the topics on offer for Phd students:

1. Bayesian spatial modelling for biodiversity (collaboration with Prof Andrew Leitch and Royal Botanical Gardens, Kew)
   Many models assume that observations are obtained independently of each other.
   However, distance between observations can be a source of correlation, which needs to be
   accounted for in any model. For example, pollution has a spatial smooth pattern and
   measurements close in space are likely to be very similar. Spatial models therefore have to
   take into account the spatial autocorrelation in datasets in order to separate the general
   trend (usually depending on some covariates) from the purely spatial random variation.
   This project will focus on developing and applying Bayesian spatial and spatio–temporal
   modelling techniques to enhance our understanding of the association between, and
   predict, plant species that are at risk of extinction and areas in need of protection in the face
   of climate change, changing land use (especially agriculture) and pollution. The pollutants of
   interest are nitrogen and phosphate–based fertilizers. We will leverage spatial distribution
   data for the entire British flora, studying changing trends in distribution and land use over
   60 years. We will also include data for a range of different measures of genomic diversity
   (e.g. genome size and polyploidy) together with climate and soil data to uncover the role of
   biological and abiotic factors in predicting species at risk of extinction, and landscapes at
   increased risk of biodiversity loss under differing land use and climate change scenarios. The
   research will be undertaken in collaboration with Dr Ilia Leitch, Senior Research Leader at
   the Royal Botanic Gardens, Kew. One statistical challenge that arises is that the data are available at different resolutions,  and advanced methods are required to model misaligned spatial and spatio–temporal data.

   We will leverage recent work by Dr Silvia Liverani on Bayesian methods for misaligned areal
   data, and extend them to meet the needs of this research challenge in the study and
   understanding of biodiversity.

2. Bayesian modelling for misaligned spatio-temporal data (with Prof Peter Congdon)
   This project will focus on Bayesian spatial modelling techniques to examine the association between measures of population health (such as hospitalisations and mortality) and socio-economic factors. This will be accomplished by developing spatial and spatio-temporal models which can allow for spatially varying coefficients, spatially adaptive priors, and spatial quantile regression.
3. Calculating and communicating partition uncertainty
   Clustering models are used to identify subsets of the data such that objects in the same group (called a cluster) are more similar, in some sense, to each other than to those in other clusters. Many widely used clustering models are defined by a set of parameters, whose uncertainty can be quantified. However, the output of a clustering model is a partition – the allocation of each object to clusters – and the uncertainty of the partition as a whole is usually overlooked, due to the size and complexity of the partition space. The aims of this PhD project are to develop a framework for calculating partition uncertainty for clustering methods and to develop methods to communicate the partition uncertainty effectively to end users.

Drop me an email if you are interested in any of the projects above. Alternatively, feel free to pitch your own project. Contact me at s.liverani@qmul.ac.uk