@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 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 nite dimensional rep- resentation. 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}, 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 understand- ing of data. When clustering functional data, most methods have used traditional clustering techniques on a vector of estimated basis coecients, 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 pro- pose diers in this respect: we employ a model that does not assume that any of the signal functions are truly identical. We cluster each signal coecient using conditionally independent Dirichlet process priors, which leads to exact match- ing of local features, represented by coecients in a multiresolution wavelet basis. We then demonstrate the method using two datasets from dierent elds to show broad application potential.}, number={1}, journal={BAYESIAN ANALYSIS}, author={Suarez, Adam Justin and Ghosal, Subhashis}, year={2016}, month={Mar}, pages={71–98} }