Bayesian Curve Classification Using Wavelets

Abstract

We propose classification models for binary and multicategory data where the predictor is a random function. We use Bayesian modeling with wavelet basis functions that have nice approximation properties over a large class of functional spaces and can accommodate a wide variety of functional forms observed in real life applications. We develop an unified hierarchical model to encompass both the adaptive wavelet-based function estimation model and the logistic classification model. We couple together these two models are to borrow strengths from each other in a unified hierarchical framework. The use of Gibbs sampling with conjugate priors for posterior inference makes the method computationally feasible. We compare the performance of the proposed model with other classification methods, such as the existing naive plug-in methods, by analyzing simulated and real data sets.