Using marked point processes for the change-point problem
Résumé
This work presents a general framework for the signal multiple change-point analysis. The proposed methodology allows one to estimate the number of change-points, their location and the length of the associated transient signals. It consists in considering that the configuration of the transient signals is the realization of a marked point process. Within this framework, the point represents the location of a change-point induced by the transient signal occurrence, whereas the mark corresponds to the transient signal length. Such a modelization allows one to include strong geometrical constraints on the configuration to be detected. The process is defined from a combination of several energy terms. Firstly, a data energy term which controls the localization of the occurrences with respect to the data. This energy can be derived from the likelihood of the observations, if available, or more generally from any contrast measure. Secondly, prior information is given by intern energy terms corresponding to geometrical constraints on the configuration to be detected. Finally, the configuration of the global minimum energy is derived thanks to a Reversible Jump Markov Chain Monte Carlo dynamics and a simulated annealing scheme. Typical applications that are investigated include "arc-tracking" detection from common three-phase supply voltage signals.