Dr Jian Qing Shi, University of Newcastle

Curve Prediction and Clustering using Mixtures of Gaussian Process Functional Regression Models

The problem of large data is one major statistical challenges, for example, more and more data are generated from subjects with different backgrounds at an incredible rate in one of our biomechanical project as well as some many other examples.  For such functional/longitudinal data, it is more flexible and efficient to treat them as curves, and flexible mixture models are capable of capturing variation and biases for the data generated from different resources.  Mixture models are also applicable to classification and clustering of the data.

In this talk, I will first introduce a nonparametric Gaussian process functional regression (GPFR) model, and then discuss how to extend to a mixture model to address the problem of heterogeneity with multiple data types.  A mew method will be presented for modelling functional data with 'spatially' indexed data, ie, the heterogeneity is dependent on factors such as region and individual patient's information.  Nonparametric and functional mixture models have also been developed for curve clustering for some very complex systems which the response curves may depend on a number of functional and non-functional covariates.  Some numerical results with simulations study and real applications will also be present.