In many applications data is collected over time or can be ordered with respect to some other criteria (e.g. position along a chromosome). Often the statistical properties, such as mean or variance, of the data will change along data. This feature of data is known as non-stationarity. An important and challenging problem is to be able to model and infer how these properties change. Examples occur in environmental applications (e.g. detecting changes in ecological systems due to climatic conditions crossing some critical thresholds), signal processing (e.g. structural analysis of EEG signals), epidemiology (e.g. early detection of hospital infections from changes in patientís antibody levels), bioinformatics (e.g. detecting changes in copy number variation), and finance (e.g. changing volatility). As technology advances, and ever larger and complex data are collected, the need to model changes in the statistical properties of the data, and the difficulty of making inference for these models increases.
Two possibilities for modelling non-stationarity are changepoint models and locally-stationary models. The former splits data into segments, where the statistical properties of the data is the same within a segment, but changes between segments. These are often appropriate for applications with abrupt changes. By comparison, locally-stationary models are based on stochastic processes where the statistical properties vary more smoothly. These two approaches are thus complementary. To date research within both areas is generally carried out independently of the other.
The main themes of the programme will be:
- to explore links and synergy between changepoint and locally-stationary models, methods for inference and the associate theory;
- to develop (computationally) efficient inference methods, that can be applied to large data, and complex models in modern scientific applications; and
- to develop associated statistical theory, that will impact on the application of these models and methods.
A focus of the programme will be the application of these methods, particularly within finance, energy and environment, and biomedical sciences.