A Bayesian study of temporal changes in seismicity

The q-exponential distribution, solution of a maximum entropy problem in the frame of nonextensive statistical mechanics, is useful for describing complex, non-linear dynamic systems that emerge in many applications of environmental and social sciences, including seismology. In this study we analyze the seismic sequence of L'Aquila earthquake and investigate the ability of the q-exponential probability distribution to grasp the temporal variations of some seismic parameters, such as magnitude and spatial location of the epicentres. Bayesian inference is performed by processing data on sliding time windows, such that each window has a fixed number of events and shifts at each new event. Other distributions (tapered Pareto, generalized gamma) are also considered and the best fitting distribution in each time window is selected by comparing the evaluated values of the posterior marginal likelihood. We found that the best fitting distribution varies over time and can be a further indicator of the activation state of the systems.