Sparsity Likelihood for Sparse Signal and Change-point Detection

We propose here sparsity likelihood scores for sparse signal detection and segmentation of multiple sequences with sparse change-points. The scores achieve the same optimality as the higher-criticism and Berk-Jones test statistics in sparse signal detection. We extend its optimality to sparse change-point estimation and detection, for both normal and Poisson models, with asymptotics that differ for the two models. We illustrate its application on simulated datasets as well as on a single-cell copy number dataset taken from a mixture of normal and tumor cells of the same cancer patient.