标题： 空间-时间点过程的残差分析方法及其在加利福尼亚地震预测模型中的应用 显示英文标题

标题： Residual analysis methods for space--time point processes with applications to earthquake forecast models in California

摘要： 现代用于空间-时间点过程模型残差分析的强效方法被回顾和比较。这些方法应用于加利福尼亚地震预测模型，这些模型用于可预测性地震研究协作中心（CSEP）。以前曾使用简单的低效方法如L检验和N检验来评估这些地震预测模型。我们则提出基于重标、稀疏化、叠加、加权K函数和偏差残差的残差方法。重标残差可用于评估模型的整体拟合情况，但与稀疏化和叠加一样，当条件强度$\lambda$波动较大时，重标通常不切实际。虽然残差稀疏化和叠加可能有助于识别模型拟合较差的空间位置，但当模型条件强度在观测区域内某些地方极低或极高时，这些方法的效力有限，而这在地震预测模型中是常见的情况。一种最近提出的稀疏化和叠加的混合方法，称为超稀疏化，是一种更有效的替代方法。 显示英文摘要

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 $\lambda$ 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.