Novel Wavelet Methods for the Analysis of Multivariate Signals
Recent advances in sensor technology have led to the collection of high-dimensional datasets from multiple sources, for example sophisticated biomedical images or 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 across time or space. Recently, wavelet models for such 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.
More recently, there have been approaches for modelling nonstationary data in the literature using wavelet packets, motivated by the availability of multiple time-frequency representations. However, this has been limited to the one-dimensional time series setting.
The aim of this project is to investigate whether wavelets packets can eliciting more information from signals to bring improved modelling capability in other contexts. In particular, we will look to extend the aforementioned work to the two-dimensional and multivariate signal settings. More specifically, we wish to develop, implement and trial wavelet packet models in a range of statistical applications, for example time dimension reduction, image registration and time series forecasting.
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.
1. Cardinali, A. and G. P. Nason (2017). Locally stationary wavelet packet processes: basis selection and model fitting. J. Tim. Ser. Anal. 15, 151–174.
2. Cardinali, A. and G. P. Nason (2018). Practical powerful wavelet packet tests for second-order stationarity. Appl. Comput. Harm. Anal. 44, 558–583.
3. Taylor, S., I. A. Eckley, and M. A. Nunes (2017). Multivariate locally stationary 2d wavelet processes with application to colour texture analysis. Stat. Comput 27, 1129–1143.
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