Bayesian analysis of temporal changes in the probability distribution of seismic parameters and links with the seismic cycle

In the frame of nonextensive statistical mechanics, the q-exponential probability distribution arises from the maximization of the Tsallis entropy under appropriate constraints (Tsallis, J. Stat. Phys., 1988). The Tsallis entropy, unlike the Boltzmann-Gibbs entropy, is non-additive and more suitable to describe complex systems far from equilibrium and with possible long-range interactions. These features have suggested several studies on earthquakes as complex system (e.g. Vallianatos et al., Proc. R. Soc. A, 2016, and references therein). In this study we assume the q-exponential probability distribution for the analysis of the temporal variations of some seismic parameters (e.g. magnitude, spatial location of the epicentres) in earthquake sequences of Italy. Bayesian inference is performed by processing data on sliding time windows, such that each window has a fixed number of events (100 in this study) and shifts at each new event (Rotondi et al., J. Geopys. Int., 2022). Other distributions (e.g. tapered Pareto, generalized gamma) are also considered and the best fitting distribution in each time window is selected by comparing the estimated 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 (Rotondi and Varini, Front. Earth Sci., 2022).