Comment on "The Maximum Possible and the Maximum Expected Earthquake Magnitude for Production-Induced Earthquakes at the Gas Field in Groningen, The Netherlands" by Gert Zoller and Matthias Holschneider

Zoller and Holschneider (2016) focused on distribution of the earthquake maximum magnitude of the gas field in Groningen, The Netherlands, and applied the predictive distribution. They incorrectly used the term Bayesian posterior probability density function because it is a term of the Bayesian parameter inference and not for the predictive distribution of a random variable. As explained here, the approach of the predictive distribution can be applied on Bayesian and frequentist inference. However, it is not a useful and stable approach. The original intention of the approach was a model test and not an actual prediction. The authors did not use the approach consequently because they did not consider the uncertainty of all parameters. Besides, the distribution of the maximum magnitude does not include more information than the magnitude frequency function (Gutenberg- Richter relation). Additionally, the state-of-the-art of mathematical statistics includes more methods for the upper bound magnitude (maximum possible earthquake magnitude), than considered by Zoller and Holschneider (2016). Uncertainty quantification is possible for these estimators, in contrast to the statement of the authors. At the end of their analysis, they used the 90% percentile (confidence level) as point estimation for the upper bound magnitude. The selection of 90% is debatable. The most recent point estimation of Beirlant et al. (2017) for the upper bound leads to a distribution of themaximum earthquake magnitude which is very different from the results of Zoller and Holschneider (2016).