标题： 基于ETAS的地震预测inlabru 显示英文标题

标题： Earthquake Forecasting with ETAS.inlabru

摘要： ETAS模型目前在地震预测领域是最受欢迎的。 MCMC方法耗时且受参数相关性的限制，同时带来参数不确定性。 基于INLA的方法"inlabru"解决了这些问题，并在贝叶斯推断中表现更好。 报告介绍了ETAS模型的组成，然后提供了模型的对数似然函数，并使用泰勒展开和分箱策略对其进行近似。 我们还介绍了inlabru中贝叶斯推断的一般过程。 报告进行了三个实验。 第一个实验探讨将一个参数固定在其实际值或错误值上对其他参数后验分布的影响。 我们发现$\alpha$和$K$存在明显的相互影响关系。 同时，将$\alpha$或$K$固定在其实际值可以将模型拟合时间减少一半以上。 第二个实验比较了真实数据和合成目录中的归一化事件间时间分布。 真实数据和合成目录的归一化事件间时间分布是一致的。 与Exp(1)相比，它们有更多短时间和长时间的事件间时间，表明存在聚集性。 对$\mu$和$p$的变化会影响事件间时间分布。 在最后一个实验中，我们使用主震前的事件来预测主震后十周的事件。 我们使用数量测试和连续排名概率评分(CRPS)来衡量预测的准确性和精确性。 我们发现我们需要至少一个主震及其相应的子震才能进行可靠的预测。 而且，当我们的数据中有更多的主震时，我们的预测会更好。 此外，我们还弄清楚了为了获得每个参数的良好后验分布需要什么。 显示英文摘要

摘要： The ETAS models are currently the most popular in the field of earthquake forecasting. The MCMC method is time-consuming and limited by parameter correlation while bringing parameter uncertainty. The INLA-based method "inlabru" solves these problems and performs better at Bayesian inference. The report introduces the composition of the ETAS model, then provides the model's log-likelihood and approximates it using Taylor expansion and binning strategies. We also present the general procedure of Bayesian inference in inlabru. The report follows three experiments. The first one explores the effect of fixing one parameter at its actual or wrong values on the posterior distribution of other parameters. We found that $\alpha$ and $K$ have an apparent mutual influence relationship. At the same time, fixing $\alpha$ or $K$ to its actual value can reduce the model fitting time by more than half. The second experiment compares normalised inter-event-time distribution on real data and synthetic catalogues. The distributions of normalised inter-event-time of real data and synthetic catalogues are consistent. Compared with Exp(1), they have more short and long inter-event-time, indicating the existence of clustering. Change on $\mu$ and $p$ will influence the inter-event-time distribution. In the last one, we use events before the mainshock to predict events ten weeks after the mainshock. We use the number test and Continuous Ranked Probability Score (CRPS) to measure the accuracy and precision of the predictions. We found that we need at least one mainshock and corresponding offspring to make reliable forecasting. And when we have more mainshocks in our data, our forecasting will be better. Besides, we also figure out what is needed to obtain a good posterior distribution for each parameter.