论文标题
半参数贝叶斯对空间地震的预测
Semiparametric Bayesian Forecasting of Spatial Earthquake Occurrences
论文作者
论文摘要
自我激发的鹰程过程用于模拟在时空聚集的事件，并以气候类型的余震序列（ETAS）模型的名义对地震学进行了广泛的研究。在ETAS框架中，假定地理区域中主震震的发生遵循不均匀的空间点过程，然后通过单独的触发核进行建模余震事件。 ETAS模型的大多数研究都取决于模型参数的点估计值，这是由于似然函数的复杂性以及估计适当的主震分布的困难。为了考虑估计的不确定性，我们提出了一种完全贝叶斯模型的贝叶斯公式，该公式在捕获空间主震过程之前使用非参数dirichlet工艺混合物。由于主震和触发过程的参数的强相关性，因此对所得模型的直接推断是有问题的，因此我们相反使用辅助潜在可变例程来执行有效的推断。
Self-exciting Hawkes processes are used to model events which cluster in time and space, and have been widely studied in seismology under the name of the Epidemic Type Aftershock Sequence (ETAS) model. In the ETAS framework, the occurrence of the mainshock earthquakes in a geographical region is assumed to follow an inhomogeneous spatial point process, and aftershock events are then modelled via a separate triggering kernel. Most previous studies of the ETAS model have relied on point estimates of the model parameters due to the complexity of the likelihood function, and the difficulty in estimating an appropriate mainshock distribution. In order to take estimation uncertainty into account, we instead propose a fully Bayesian formulation of the ETAS model which uses a nonparametric Dirichlet process mixture prior to capture the spatial mainshock process. Direct inference for the resulting model is problematic due to the strong correlation of the parameters for the mainshock and triggering processes, so we instead use an auxiliary latent variable routine to perform efficient inference.
