Curve prediction and clustering with mixtures of Gaussian process functional regression models

Shi et al. (2006) proposed a Gaussian process functional regression (GPFR) model to model functional response curves with a set of functional covariates. Two main problems are addressed by this method: modelling nonlinear and nonparametric regression relationship and modelling covariance structure and mean structure simultaneously. The method gives very good results for curve fitting and prediction but side-steps the problem of heterogeneity. In this paper we present a new method for modelling functional data with ‘spatially’ indexed data, i.e., the heterogeneity is dependent on factors such as region and individual patient’s information. For data collected from different sources, we assume that the data corresponding to each curve (or batch) follows a Gaussian process functional regression model as a lower-level model, and introduce an allocation model ∗Address for correspondence: School of Mathematics and Statistics, University of Newcastle, NE1 7RU, UK. Email: [email protected]