时空点过程的残差分析方法及其在加州地震预报模型中的应用
Residual analysis methods for space--time point processes with applications to earthquake forecast models in California
摘要：
现代，强大的技术的残差分析的时空点过程模型进行了审查和比较。这些方法被应用到加州地震预测模型中使用的地震可预测性研究合作实验室（CSEP）。这些地震预测模型的评估以前已经使用简单的，低功耗的手段，如L-测试和N-测试。相反，我们提出了基于重新缩放，细化，叠加，加权K函数和偏差残差的残差方法。重缩放残差可用于评估模型的总体拟合，但与细化和叠加一样，当条件强度$λ$不稳定时，重缩放通常不切实际。虽然残余细化和叠加可能有助于识别模型拟合不佳的空间位置，但当建模的条件强度假设在观测区域的某个地方极低或极高时，这些方法的能力有限，这通常是地震预测模型的情况。最近提出的细化和叠加的混合方法，称为超细化，是一个更强大的替代方案。
英文摘要：
Modern, powerful techniques for the residual analysis of spatial-temporal point process models are reviewed and compared. These methods are applied to California earthquake forecast models used in the Collaboratory for the Study of Earthquake Predictability (CSEP). Assessments of these earthquake forecasting models have previously been performed using simple, low-power means such as the L-test and N-test. We instead propose residual methods based on rescaling, thinning, superposition, weighted K-functions and deviance residuals. Rescaled residuals can be useful for assessing the overall fit of a model, but as with thinning and superposition, rescaling is generally impractical when the conditional intensity $λ$ is volatile. While residual thinning and superposition may be useful for identifying spatial locations where a model fits poorly, these methods have limited power when the modeled conditional intensity assumes extremely low or high values somewhere in the observation region, and this is commonly the case for earthquake forecasting models. A recently proposed hybrid method of thinning and superposition, called super-thinning, is a more powerful alternative.
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