Rejoinder

Huijing Jiang, Business Analytics and Mathematical Sciences and Nicoleta Serban, Georgia Institute of Technology, present a model methodology on clustering functional data under spatial interdependence. In their model, the local neighborhood dependence is only considered as a prior while the final clustering membership estimation is based on its posterior probability. Under a large number of sample time points for each random function, information in the likelihood should overweigh the prior information and result in accurate posterior probability estimates. The authors approach does not restrict to the use of the B-spline/P-spline basis of functions. The wavelet basis decomposition will model local irregularities in the random functions, and therefore, the small differences among the signal functions may be detected by the algorithm.