### Bayesian and Frequentist Approaches for the Estimation of the Maximum Expected Earthquake Magnitude in Iran

#### Abstract

The maximum earthquake magnitude plays a crucial role in different aspects of seismic hazard and risk assessments. Previous work by Salamat et al. [1] shows the divergence of the confidence interval of the maximum possible earthquake magnitude M(max )for high levels of confidence 1-α, in different seismotectonic zones of Iran. For this, M_(max ) is replaced by the maximum expected earthquake magnitude μ_t that is calculated for different predefined future time intervals〖 T〗_f. In this work, the frequentist and Bayesian approaches are applied to calculate the upper bound of the confidence interval of 〖 μ〗_t. The frequentist confidence intervals are calculated for the level of confidence 1-α=95% and 99%, and future time intervals T_f=30,50 years. In the Bayesian approach, the posterior distributions of the maximum expected earthquake magnitude are calculated for T_f=30,50 years and 90% confidence level. The stationary Poisson process in time and Gutenberg Richter relation are assumed as a statistical model for the magnitude distribution. In order to estimate μ_t in each seismotectonic zone, three different scenarios of M_max=8.5,9.0,9.5 are assumed. In order to find the influence of the declustering, all calculations are applied for both original and declustered catalogs. The results show, as long as the length of the time interval is short or moderate, different values of〖 M〗_max have a minor effect on the estimation of the maximum expected earthquake magnitude μ_t.

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