University of Washington - Department of Statistics
A number of different scientific fields ranging from biomedicine to economics, to molecular biology, generate functional data. The statistical analysis of a sample of curves, known as Functional Data Analysis (FDA), has as one of its goals explaining how variation in the functional outcome can be explained by some predictors. However, these curves tend to be misaligned, exhibiting variation not only in amplitude, but also in phase. Teasing apart these sources of variation is a central issue in FDA. Oftentimes, alignment procedures are used to pre-process the data before applying standard multivariate analysis techniques. In this dissertation we discuss the analysis of a sample of curves from a Bayesian perspective, providing methods for curve registration and functional regression. We assess our methods using simulation studies. Moreover, we apply our models to some datasets. In particular, we use our models to infer gene-network relationships utilizing time course microarray data. Our inferences are based on Markov Chain Monte Carlo samples from the posterior distribution of the functions of interest.