School of Mathematics & Statistics

Information about postgraduate research opportunities and how to apply can be found on the Postgraduate Research Study page. Below is a selection of projects that could be undertaken with our group.

Biodiversity Monitoring Using Deep Learning Under Ground Truth Uncertainty: Supporting Conservation of Wandering Albatrosses and Hedgehogs (PhD)

Supervisors: Tiffany Vlaar, Ellen Bowler (BAS), Philip Stephens (Durham), Linus Ericsson (Computing Science), Peter Fretwell (BAS)
Relevant research groups: Machine Learning and AI, Environmental, Ecological Sciences and Sustainability, Imaging, Image Processing and Image Analysis

Full project description and information on how to apply: IAPETUS DTP Website.

Technological advances have led ecology into its big data era. Although this offers exciting opportunities for biodiversity monitoring, the volume of data requiring manual processing poses a significant challenge. Popular solutions to this challenge: deep learning and citizen science approaches, have various limitations, but their combination may offer an effective and reliable way forward (e.g. for counting wildlife in aerial survey images Torney et al., 2019 and camera trap data Green et al., 2020). Humans are highly data-efficient compared to deep learning approaches, and there remain fundamental differences between human and machine perception, e.g. in the type of errors made (Geirhos et al., 2021) and sensitivity to data corruption (Geirhos et al., 2018). In this project we will compare the performance and biases of classifications obtained through deep learning and citizen science approaches. In particular, we will focus on the setting where there is uncertainty in the labels assigned by volunteers, i.e. different annotators have provided different labels for the same image (Bowler et al. 2020; Hockerts et al. 2025). Researchers at the British Antarctic Survey (BAS) have prepared a satellite image dataset consisting of citizen science annotations of wandering albatrosses (Diomedea exulans) across 11,839 image tiles from South Georgia Island in the South Atlantic Ocean. This dataset offers an ideal opportunity to study integration of probabilistic AI and citizen science approaches when dealing with uncertainty in detection. We will study if our findings generalize to other settings, specifically to camera-trap data provided through the National Hedgehog Monitoring Programme to study the substantial decline of hedgehog (Erinaceus europaeus) numbers in the UK and corresponding citizen science classifications obtained through the MammalWeb platform. In addition, depending on the students’ interest, fieldwork can be conducted to collect drone data, to be used for further analysis.

Bayesian methods to detect nanoclustering in single molecule imaging experiments (PhD)

Supervisors: Mayetri Gupta
Relevant research groups: Modelling in Space and Time, Bayesian Modelling and Inference, Statistical Modelling for Biology, Genetics and *omics, Imaging, Image Processing and Image Analysis

Recent microscopic imaging technologies being developed now allow scientists to track and record the trajectories of individual molecules within living cells at nanometer scales over infinitesimal amounts of time. Discovering “nanoclusters” of such molecules - discrete areas within the cell (over space and/or time) which are important in terms of biological function - can give researchers an understanding into transient, functional states of cellular activity that underpin critical biological functions that may be taking place in the living organism. It can also establish how these correlate with changing experimental conditions, paving the way for future research into effective medical interventions. The high volume and density of individual molecular trajectory data, combined with the correlated and interacting trajectories of moving particles with state transitions over time, makes it challenging to accurately identify these nanoclusters over space (spatially) and over space and time (spatio-temporally), using standard statistical approaches. This project will aim to develop novel statistical visualization and clustering approaches for the detection of nanoclusters, making use of Bayesian hierarchical modelling techniques, latent variable modelling, and multi-directional block clustering methodologies, and compare and contrast the effectiveness of model-based and non-model-based clustering approaches in determining meaningful features within the data. The techniques developed can potentially be useful across fields ranging from medical genomics and imaging to diverse engineering and transportation applications.

Medical image segmentation and uncertainty quantification (PhD)

Supervisors: Surajit Ray
Relevant research groups: Machine Learning and AI, Imaging, Image Processing and Image Analysis

This project focuses on the application of medical imaging and uncertainty quantification for the detection of tumours. The project aims to provide clinicians with accurate, non-invasive methods for detecting and classifying the presence of malignant and benign tumours. It seeks to combine advanced medical imaging technologies such as ultrasound, computed tomography (CT) and magnetic resonance imaging (MRI) with the latest artificial intelligence algorithms. These methods will automate the detection process and may be used for determining malignancy with a high degree of accuracy. Uncertainty quantification (UQ) techniques will help generate a more precise prediction for tumour malignancy by providing a characterisation of the degree of uncertainty associated with the diagnosis. The combination of medical imaging and UQ will significantly decrease the requirement for performing invasive medical procedures such as biopsies. This will improve the accuracy of the tumour detection process and reduce the duration of diagnosis. The project will also benefit from the development of novel image processing algorithms (e.g. deep learning) and machine learning models. These algorithms and models will help improve the accuracy of the tumour detection process and assist clinicians in making the best treatment decisions.

Analysis of spatially correlated functional data objects (PhD)

Supervisors: Surajit Ray
Relevant research groups: Modelling in Space and Time, Computational Statistics, Nonparametric and Semi-parametric Statistics, Imaging, Image Processing and Image Analysis

Historically, functional data analysis techniques have widely been used to analyze traditional time series data, albeit from a different perspective. Of late, FDA techniques are increasingly being used in domains such as environmental science, where the data are spatio-temporal in nature and hence is it typical to consider such data as functional data where the functions are correlated in time or space. An example where modeling the dependencies is crucial is in analyzing remotely sensed data observed over a number of years across the surface of the earth, where each year forms a single functional data object. One might be interested in decomposing the overall variation across space and time and attribute it to covariates of interest. Another interesting class of data with dependence structure consists of weather data on several variables collected from balloons where the domain of the functions is a vertical strip in the atmosphere, and the data are spatially correlated. One of the challenges in such type of data is the problem of missingness, to address which one needs develop appropriate spatial smoothing techniques for spatially dependent functional data. There are also interesting design of experiment issues, as well as questions of data calibration to account for the variability in sensing instruments. Inspite of the research initiative in analyzing dependent functional data there are several unresolved problems, which the student will work on:

• robust statistical models for incorporating temporal and spatial dependencies in functional data
• developing reliable prediction and interpolation techniques for dependent functional data
• developing inferential framework for testing hypotheses related to simplified dependent structures
• analysing sparsely observed functional data by borrowing information from neighbours
• visualisation of data summaries associated with dependent functional data
• Clustering of functional data

Regular seminars relevant to the group are held as part of the Statistics seminar series. The seminars cover various aspects across the AI3 initiative and usually span multiple groups. You can find more information on the Statistics seminar series page, where you can also subscribe to the seminar series calendar.