CMStatistics 2015: Start Registration
View Submission - CMStatistics
B1766
Topic: Contributions on statistics for functional data Title: Model-based functional clustering to detect climate changes Authors:  Per Arnqvist - Umea University (Sweden) [presenting]
Sara Sjostedt de Luna - Umea University (Sweden)
Abstract: A model-based method to cluster functions into $k$ latent homogeneous groups is proposed. The functions are represented by linear combinations of known basis functions, e.g. B-splines. The (spline) coefficients are assumed to be normally distributed allowing for different mean and covariance structures for the underlying $k$ groups. Extending previous results, we derive/propose an EM algorithm to estimate the parameters of the model and the posterior probabilities used to assign group labels to each function. The model can handle unequally spaced and also different number of observations of the sampled functions. The method also opens up for incorporating covariates in the model. Information criteria, such as AIC, is suggested to determine the number of latent groups.The method is illustrated by analyzing a varved lake sediment core from the lake Kassjon (N. Sweden). The sediment record consists of around 6400 varves, each varve having a functional seasonal pattern. Image analysis was used to generate the observed data of yearly profiles (in terms of grey-scale variation) and the varying thickness was measured as the number of pixels within a varve (year).