Consideration of prior information in the inference for the upper bound earthquake magnitude

Abstract

The upper bound earthquake magnitude (maximum possible magnitude) of a truncated Gutenberg-Richter relation is the right truncation point (right end-point) of a truncated exponential distribution and is important in the probabilistic seismic hazard analysis. It is frequently estimated by the Bayesian inference. This is a non-regular case and suffers some shortcomings in contrast to the Bayesian inference for the regular case of likelihood function. Here previous non-Bayesian inference methods are outlined and discussed as alternatives including, the formulation of the corresponding confidence distributions (confidence or credible interval). Furthermore, the consideration of prior information is extended to non-Bayesian estimation methods. In addition, two new estimation approaches with prior information are developed. The performances of previous and new estimation methods and corresponding confidence distributions were studied by using Monte Carlo simulations. The mean squared error and bias were used as the main performance measures for the point estimations. In summary, previous, and new alternatives overcome the fundamental weakness of the Bayesian inference for the upper bound magnitude. These alternatives are not perfect but extend the opportunities for the estimation of the upper bound magnitude considerably, especially the consideration of prior information. A prior distribution reduces the global mean squared error but leads to a local bias...