Multiscale change-point analysis of inhomogeneous Poisson processes using unbalanced wavelet decompositions

We present a continuous wavelet analysis of count data with timevarying intensities. The objective is to extract intervals with significant intensities from background intervals. This includes the precise starting point of the significant interval, its exact duration and the (average) level of intensity. We allow multiple change points in the intensity curve, without specifying the number of change points in advance. We extend the classical (discretised) continuous Haar wavelet analysis towards an unbalanced (i.e., asymmetric) version. This additional degree of freedom allows more powerful detection. Locations of intensity change points are identified as persistent local maxima in the wavelet analysis at the successive scales. We illustrate the approach with simulations on low intensity data. Although the method is presented here in thecnotext of Poisson (count) data, most ideas (apart from the specific Poisson normaluzation) apply for the detection of multiple change poits in other circumstances (such as additive Gaussian noise) as well.