Recent advances in sensor technology have led to the collection of high-dimensional datasets from multiple sources, for example different physiological measurements in health monitoring and telemetry. These complex datasets are often also recorded over time.
Many industrial and environmental applications generate processes which are nonstationary in nature, that is exhibit observations with properties which vary over time e.g. volatility in financial markets. In addition, due to various reasons, data is often collected at different rates, e.g. heart rate / step counts from wearable sensors due to changes in activity levels, or retail data being recorded at daily, monthly or quarterly periods. However, there has been relatively little work in developing tools designed to analyse such signals.
Recently, wavelet models for nonstationary processes have been proposed in the literature, due to their ability to represent the local behaviour of signals efficiently. In particular, the locally stationary wavelet modelling framework has been effective in representing realistic characteristics of observed processes. These models have been successfully applied in a number of statistical applications of multivariate time series and image analysis, such as classification and dependence estimation.
The aim of this project is to investigate whether traditional and wavelet models can be adapted to analyse `multirate’ signals efficiently. More specifically, we will develop statistical tools for time series forecasting, changepoint detection and dimension reduction for signals with multiple sampling rates and in the `online’ (sequential analysis) setting.
The successful candidate should have a first class or 2:1 degree in Mathematics, Statistics or another relevant discipline. A Masters qualification in Statistics would be beneficial. Some familiarity with R is essential, and experience with time series modelling and / or wavelets is desirable.
Informal enquiries should be directed to Dr Matthew Nunes, [Email Address Removed].
Formal applications should be made via the University of Bath’s online application form:
Please ensure that you quote the supervisor’s name and project title in the ‘Your research interests’ section.
More information about applying for a PhD at Bath may be found here:
Anticipated start date: 30 September 2019.
Candidates may be considered for a University Research Studentship which will cover UK/EU tuition fees, a training support fee of £1,000 per annum and a tax-free maintenance allowance at the UKRI Doctoral Stipend rate (£14,777 in 2018-19) for a period of up to 3.5 years.
Wilson, R. E., Eckley, I. A., Nunes, M. A. and Park, T. (2018+) Dynamic detection of anomalous regions within distributed acoustic sensing data streams using locally stationary time series. Data Mining and Knowledge Discovery (to appear).
Eckley, I. and Nason, G. P. (2018). A test for the absence of aliasing or local white noise in locally stationary wavelet time series. Biometrika. 105, 833–848.
Nason, G. P., Powell, B.J., Elliot, D. and Smith, P. (2017). Should we sample a time series more frequently? Decision support for multirate spectrum estimation. JRSSA 180 (2), 353–407.
How good is research at University of Bath in Mathematical Sciences?
FTE Category A staff submitted: 44.40
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