School of Mathematics

Case Studies

A selection of case studies of previous work that we have been involved in.


Identifying offshore foraging areas used by seabirds

Movements of mobile animals such as seabirds are often changeable and difficult to predict. We tested whether oceanographic and environmental variables can be used to predict offshore areas used by seabirds and whether these predictions are consistent over time. We used spatial models to relate foraging locations, identified using GPS data collected from seabird foraging trips, with variables such as sea surface temperature. We found that seabird foraging areas can be predicted from environmental data, but the accuracy of these predictions do not remain consistent between years or at different stages of the breeding season.


Estimating red grouse population size using harvesting data

Red grouse are an important bird species in the UK, with grouse shooting supporting rural economies. Recently, there are concerns that grouse numbers are declining in some areas with potential repercussions for local economies. Biologists at the Game and Wildlife Conservation Trust used long-term harvesting data to estimate regional changes in grouse populations and factors influencing these changes. Generalised additive models were fitted to account for temporal trends in the data and showed that grouse populations had declined in Scotland and Wales in recent decades due to changes in land management.


Hospital patients at risk from zoonotic disease

Diseases that spread from animals to people (zoonotic diseases) are an increasing concern to public health. Some (e.g. Ebola virus disease, E.coli O157) are responsible for serious epidemics, but outbreaks are unpredictable. The Vietnam Initiative on Zoonotic Infections (VIZIONS) collected clinical and behavioural data from hospital patients in Vietnam. We analysed these data using multivariate statistical methods and mixed models to 1) identify patients most likely to have an unknown zoonotic virus; 2) identify risk factors associated with zoonotic disease. We identified one patient with a novel potentially zoonotic virus from pigs, and found that contact with pigs was a particular risk factor for zoonotic disease in Vietnam.


Change in cognitive ability over time.

Cognitive ability changes over time and declines in later years. In several studies we fit models of the trajectory to summarise the overall shape of change over time in a useful way. These models enable change to be compared between groups in order to address questions around the influence of social, demographic, lifestyle, and genetic factors on age-related change in cognitive ability. The models were used to evaluate risk factors and predictive factors for change in cognitive ability. More complex models were constructed to explore the reciprocal influence of changes in factors such as wellbeing and physical fitness on change in cognitive ability.


Vocal agitation as a predictor of emotion and stress

Speech signals can be processed to extract features such as roughness and fluctuations in pitch. These features were used to train a machine learning algorithm to evaluate levels of emotion and stress. This was used to classify levels of stress, with application in warning systems and safety monitoring.


Evaluating an instrument to assess delirium in patients in intensive care.

A new smartphone-based instrument was developed at Edinburgh Royal Infirmary to assess patients in intensive care. It was designed to measure levels of arousal in order to screen for post-operative delirium and evaluate risk of dementia and death. The instrument was validated by comparison against existing gold standard assessment methods.


Analysis of magnetic resonance imaging (MRI) of brain structures and ultrasound measurements of arterial narrowing.

An important research question concerns whether change in aging brain structure due to tissue wearing away is due to narrowing arteries that supply blood or to an as yet unknown cause. This question has direct consequences for cognitive decline, stroke, and dementia. Models were developed to show the association between progressive changes in brain structure shown by image analysis of MRI scans over a period of six years, and progressive arterial narrowing over the same period, and also change in key cognitive abilities over the same period. Results suggested that changes in brain structure, associated with cognitive decline, were not caused by narrowing arteries.


State-space models of person-situation transactions.

A novel model of personality was developed based on the idea of a state-space of personality in which each individual is represented as a multidimensional point. The model was based on the proposition that individuals move within this space under the influence of various attractors, such as other individuals for example, with the overarching purpose of striving for an equilibrium state. This model enabled simulations of various complicated social phenomena, and was able to demonstrate interesting complex interplay between individuals and their situational experiences.