Generalized Bayesian inference for domain selection in functional data

Domain selection for functional data involves the identification of subregions of the domain of the functions that carry the most informative signals. Current methodologies often suffer from partition dependency, where results are heavily influenced by a priori fixed choices of interval width and location. This paper proposes a Generalized Bayesian Inference approach for functional domain selection that treats the number of subdomains, their locations, and their widths as unknown parameters within a joint hierarchical framework. By utilizing a penalized objective function based on the Wasserstein distance and a Reversible Jump Markov chain Monte Carlo (RJ-MCMC) sampler, the model simultaneously recovers multiple disjoint intervals without requiring pre-defined partitions and widths. Application to electrocardiogram (ECG) data shows that the methodology effectively pinpoints clinically relevant heartbeat segments, such as the P-Wave and the ST-segment.