@article{suarez_ghosal_2017, title={Bayesian Estimation of Principal Components for Functional Data}, volume={12}, ISSN={["1936-0975"]}, DOI={10.1214/16-ba1003}, abstractNote={The area of principal components analysis (PCA) has seen relatively few contributions from the Bayesian school of inference. In this paper, we propose a Bayesian method for PCA in the case of functional data observed with error. We suggest modeling the covariance function by use of an approximate spectral decomposition, leading to easily interpretable parameters. We perform model selection, both over the number of principal components and the number of basis functions used in the approximation. We study in depth the choice of using the implied distributions arising from the inverse Wishart prior and prove a convergence theorem for the case of an exact finite dimensional representation. We also discuss computational issues as well as the care needed in choosing hyperparameters. A simulation study is used to demonstrate competitive performance against a recent frequentist procedure, particularly in terms of the principal component estimation. Finally, we apply the method to a real dataset, where we also incorporate model selection on the dimension of the finite basis used for modeling.}, number={2}, journal={BAYESIAN ANALYSIS}, author={Suarez, Adam J. and Ghosal, Subhashis}, year={2017}, month={Jun}, pages={311–333} }
@article{suarez_ghosal_2016, title={Bayesian Clustering of Functional Data Using Local Features}, volume={11}, ISSN={["1936-0975"]}, DOI={10.1214/14-ba925}, abstractNote={The use of exploratory methods is an important step in the understanding of data. When clustering functional data, most methods use traditional clustering techniques on a vector of estimated basis coefficients, assuming that the underlying signal functions live in the L2-space. Bayesian methods use models which imply the belief that some observations are realizations from some signal plus noise models with identical underlying signal functions. The method we propose differs in this respect: we employ a model that does not assume that any of the signal functions are truly identical, but possibly share many of their local features, represented by coefficients in a multiresolution wavelet basis expansion. We cluster each wavelet coefficient of the signal functions using conditionally independent Dirichlet process priors, thus focusing on exact matching of local features. We then demonstrate the method using two datasets from different fields to show broad application potential.}, number={1}, journal={BAYESIAN ANALYSIS}, author={Suarez, Adam Justin and Ghosal, Subhashis}, year={2016}, month={Mar}, pages={71–98} }