From Hypothesis Testing to Bayesian Model Comparison: Rigorous Tools to Characterize Earthquake Recurrence

There is quite some debate in the earthquake community about the complexity of the recurrence models that should be considered to describe the recurrence of events on given faults. The null-hypothesis testing approach seems to be favored as more rigorous and conservative, in particular for hazard assessment purposes, whereas still few Bayesian applications have been demonstrated. We do not only want to review the mathematical and philosophical bases for Bayesian methods, but we want to emphasize how constructive such a model-based approach can be to problem solving when the traditional datasets (earthquake dates) are short and have missing data. What shall we do when a p-value test does not reject a simple model ? it is not very informative to know that one hypothesis can not be rejected. It is not much more informative to list all hypotheses which can not be rejected, for a given p value and a given dataset. It is much more informative to compare the relative performances of the different models (hypotheses), given our current knowledge. The rigorous framework for such model comparison is the Bayesian framework. This framework also makes the use of physical models easy. This is important since more complex models can be more physics-based and be sequentially constrained by additional datasets.