My research interests can broadly be described under the heading of time-series analysis. More specifically, I work on high-dimensional statistics/time-series, optimisation algorithms (usually convex), and spectral analysis with locally-stationary wavelet models.
Theory/Methodology
Theoretical aspects of my research relate to the specification and estimation of stochastic processes. Novel aspects of this work revolve around both issues of non-stationarity, and/or high-dimensionality.
I am especially interested in the role of model-selection in increasing the efficiency of statistical estimation in the presence of structural assumptions (i.e. sparsity) on the process representation. Modern M-estimation frameworks allow an interesting connection to Bayesian prior specification, whilst enabling efficient computational approaches to perform point estimation. I am interested in both how optimisation (computational) and statistical (estimator) related errors affect our ability to recover model structure.
Application
I am interested in data-rich domains which can take advantage of advances in high-dimensional time-series methodology. This may be in either a descriptive (i.e. clustering), or predictive setting. Generally, applications constitute the analysis of complex systems, for instance the brain, via monitoring large numbers of data-streams, i.e. voxels in fMRI images, EEG traces, or even individual (or localised) neuronal firing.
Applications I am currently working on include:
- Identifying partial correlation graphs from aggregated fMRI data in order to understand brain interaction and how this is associated with task/brain state
- Analysing wind-turbine/farm behaviour to detect anomalies and characterise performance
- Assessing correlations between packet flows to understand computer network behaviour
CFAS420 Statistical Learning
