Measures of uncertainty for the number of change points selection

In the field of multiple change-point analysis, methodologies are typically divided based on whether the number of changes is known beforehand. Consequently, a significant challenge arises in accurately determining the number of change points, which can be reframed within the model selection framework. In this paper, we introduce a novel perspective on the measure of uncertainty regarding the selection of the number of change points. We develop a framework to construct a confidence interval for the number of change points for a given detection approach. Moreover, we propose the LogP measure to assess the accuracy of the selection procedure. The theoretical properties and empirical significance of the blocky sequence model are discussed in detail. Furthermore, the efficacy of the proposed measure is demonstrated through Monte Carlo simulations, and an application on neuroblastoma data is presented, illustrating the performance of our proposed method in practice.