Bayesian Approach for Estimating the Distribution of Magnitudes, Interevent Times and Distances of Earthquake Sequences

A Bayesian approach has been applied to estimate the distribution of magnitudes, interevent distances and times of earthquakes occurred in 2017 in central Italy by using a small amount of random samples drawn from the distribution of the same seismic parameters for the earthquakes occurred in 2014-2016. We applied the method to the whole and aftershock-depleted seismicity by using the exponential and the normal model to fit the distributions of the seismic parameters. Our findings indicate that the exponential model fits the distributions of the seismic parameters much better than the normal model. Furthermore, in the whole seismicity case, the method requires at least 2100 to 2300 random samples to estimate the distributions of the seismic parameters of earthquakes occurred in 2017 with an estimation error less than 0.01; while in the aftershock-depleted case, a minimum number of random samples varying between 360 and 1470 occurred in 2014-2017 is required to estimate the distributions of the seismic parameters of earthquakes occurred in 2017 with an estimation error less than 0.01.