Multiscale change point analysis in Poisson count data

Abstract

Motivated by the application of single molecule detection in a highly dilute solution, we discuss the problem of multiple change point detection in the intensity curve of low-intensive Poisson observations. It is explained that the multiple change point detection problem is inherently a multiscale problem. We analyze the data using an extension of the Continuous Wavelet Transform (CWT), the so-called Unbalanced Wavelet Transform. The presence of change points in the underlying intensity curve is revealed by a multiscale chain of local maxima in the CWT analysis. We present a new algorithm for the reconstruction of the chains by linking local maxima across scales. The new algorithm outperforms the existing ones in case of low-intensive signals, where noisy fluctuations are relatively dominant. Low intensities also motivate the extension of the CWT towards the Unbalanced Wavelet Transform. This extension is crucial in detecting small changes against intensive noise.