Bayesian local clustering of functional data via semi-Markovian random partitions

Abstract: We introduce a Bayesian framework for indirect local clustering of functional data, leveraging B-spline basis expansions and a novel dependent random partition model. By exploiting the local support properties of B-splines, our approach allows partially coincident functional behaviors, achieved when shared basis coefficients span sufficiently contiguous regions. This is accomplished through a cutting-edge dependent random partition model that enforces semi-Markovian dependence across a sequence of partitions. By matching the order of the B-spline basis with the semi-Markovian dependence structure, the proposed model serves as a highly flexible prior, enabling efficient modeling of localized features in functional data. Furthermore, we extend the utility of the dependent random partition model beyond functional data, demonstrating its applicability to a broad class of problems where sequences of dependent partitions are central, and standard Markovian assumptions prove overly restrictive. Empirical illustrations, including analyses of simulated data and tide level measurements from the Venice Lagoon, showcase the effectiveness and versatility of the proposed methodology.