Assessing seismic risk in low-to-moderate seismic activity areas like French mainland is a challenge. In these areas, the estimation of large earthquake hazard calls for models driven by sparse observation data and interpretative seismic knowledge. This leads models used in probabilistic seismic hazard assessment (PSHA) and declustering algorithms to large epistemic uncertainties that are overrepresented due to the large amount of parameters used in it. To concentrate epistemic uncertainties into one single method, we intend to limit the number of parameters under consideration by using the non-parametric inter-event time method. This method is empirical and needs a lot of data to be accurate. In the context of sparse large earthquake data, this paper proposes an implementation of the inter-event time method that ensures the stability of main shock proportions for sparse seismic data. We call this implementation magnitude of inferred main shock proportion (MIMP). This method is applied to the historical French seismic catalogue. We use a Monte Carlo Markov Chain to sample the whole space of magnitude uncertainties contained in this catalogue. We produce a set of equiprobable main shock proportion–magnitude and frequency–magnitude distributions. Results are discussed in the light of reference works published in the literature.

在像法国大陆这样的中低度地震活动区评估地震风险是一个挑战。在这些地区，对大地震灾害的估计需要建立由稀疏观测数据和解释性地震知识驱动的模型。这导致概率地震危险性评估（PSHA）和聚类算法中使用的模型导致大量的认识不确定性，由于其中使用了大量参数，这些不确定性被过分表示。为了将认知不确定性集中到一种方法中，我们打算通过使用非参数事件间时间方法来限制所考虑的参数数量。此方法是经验性的，需要大量数据才能准确。在稀疏的大地震数据的背景下，本文提出了一种事件间时间方法的实现方法，该方法可以确保稀疏地震数据的主要冲击比例的稳定性。我们称这种实施推断的主震比例的大小（MIMP）。此方法适用于法国历史地震目录。我们使用蒙特卡洛马尔可夫链对本目录中包含的幅度不确定性的整个空间进行采样。我们产生了一组等概率的主震比例-幅值和频率-幅值分布。根据文献中发表的参考文献讨论了结果。