Some reasoning on the RELM-CSEP likelihood-based tests

The null hypothesis is the essence of any statistical test: this is basically a comparison of what we observe with what we would expect to see if the null hypothesis was true. In this work, I explore the suitability of the null hypothesis of likelihood-based tests (LBTs), which are often adopted by the laboratories of the Collaboratory for the Study of Earthquake Predictability (CSEP), to check earthquake forecast models. First, I discuss the LBT in the wider context of classical statistical hypothesis testing. Then, I present some cases in which the null hypothesis of LBT is not appropriate for determining the merits of earthquake forecast models. I justify these results from a theoretical point of view, within the framework of point process theory. Finally, I propose a possible upgrade of LBT to enable the correct assessment of the forecasting capability of earthquake models. This study may provide new insights to the CSEP LBT.