On the examination of a criticality measure for a complex system in a forecasting perspective

Many complex phenomena concerning extreme events causing natural disasters exhibit power-law behavior, reflecting a hierarchical or fractal structure. These phenomena seem to be susceptible to description using approaches inspired by statistical mechanics, particularly approaches involving generalizations of the classical concept of entropy. In this framework we consider the nonextensive Tsallis entropy; by its constrained optimization we derive the expression of the q- exponential distribution which controls the behavior of variables that, in geophysics, can be for instance seismic moment, length of faults, and inter-event times. We estimate the model parameters in the Bayesian perspective and apply this approach to the identification of different dynamical regimes in seismic sequences.