1. Stochastic modelling and object oriented data analysis: This project develops a novel statistical methodology to analyse tree-like data (brain artery trees) based on a topological data representation. Standard methods try to extract high dimensional features from the representation for further analysis. This project considers a stochastic modelling approach similar to queueing models for statistical inference.
2. Prediction models for continuous monitoring data: It is easy to continuously collect and monitor various signals such as physiological or health related information, but is challenging to build a statistical model that takes such information into account. One can view such data as high-dimensional time series but there is more structural information/constraint that can be exploited. This project focuses on developing novel statistical methods using the ideas from functional data analysis and sparsity estimation.
3. Multivariate functional data analysis: Multivariate analysis is well developed for vector-like data, but not well developed for curve-like data such as continuous signals or functional data. Especially capturing (non-linear) dependence in high dimensional setting is challenging due to the inherent geometry of the data. This project develops novel statistical methods that combine the analytical (functional data analysis) and geometrical (shape analysis) approaches to analysing such type of data.
4. Spatial functional data and network regularisation: The spatial data has a natural network structure that is linked to each other through neighbours. When the dimension is high and the information is incomplete, it is difficult to estimate the underlying structure. This project considers to incorporate network regularisation methods in the context of spatial data analysis to tackle statistical inference problems.
My main research area centres around functional data analysis and its applications. A typical functional data will be in the form of curves, or densely observed longitudinal data, such as spectrometric curves or cardiac frequency profiles. I focus on semi- or non-parametric approaches to analysing such data. Recent works are motivated by the need of developing methodologies for the analysis of multi-dimensional curves based on dynamic relations, and for extending to more general objects such as shapes or images.
Data as curves can also arise as intermediary from other forms of data, for example, risk neutral density functions, mortality curves, periodograms or intensity functions, and many nonparametric and functional data analysis techniques can be adopted to these type of data.
My interest also extends to regression models for extreme events, multiple point process models, ordinary differential equation models and medical statistics. In particular I am interested in extending these models to incorporate more complex data structure or high dimensional problems.
