Universal features of correlated bursty behaviour

Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty behavior has been characterized by a fat-tailed inter-event time distribution, while temporal correlations were measured by the autocorrelation function. However, these characteristic functions are not capable to fully characterize temporally correlated heterogenous behavior. Here we show that the distribution of the number of events in a bursty period serves as a good indicator of the dependencies, leading to the universal observation of power-law distribution in a broad class of phenomena. We find that the correlations in these quite different systems can be commonly interpreted by memory effects and described by a simple phenomenological model, which displays temporal behavior qualitatively similar to that in real systems

Wavelet-Based Nonparametric Bayes Methods

In this chapter, we will provide an overview of the current status of research involving Bayesian inference in wavelet nonparametric problems. In many statistical applications, there is a need for procedures to (i) adapt to data and (ii) use prior information. The interface of wavelets and the Bayesian paradigm provide a natural terrain for both of these goals