基于轮廓似然估计的广义极值分布在地震中长期预测中的应用

为描述强震预测的不确定性，在地震预报极值分析模型的参数估计中，引入轮廓似然估计法。对广义极值分布中形状参数和地震重现水平的轮廓似然估计原理及数值算法进行了详细地阐述，并利用构建的广义极值分布模型对东昆仑地震带进行了地震危险性分析。关于形状参数和重现水平的点估计，以及10年以内的重现水平置信区间的估计，轮廓似然估计法与极大似然估计法效果基本相同，但在中长期地震重现水平置信区间的预测中，轮廓似然估计法得到的关于置信水平不对称的置信区间，在强震水平下对预测震级的不确定性表达更准确，预测结果更加有效。

Application of generalized extreme value distribution based on profile likelihood estimation in long term earthquake prediction

To describe the uncertainty of strong earthquake prediction, we introduced the profile likelihood estimation into parameter estimation of extreme value model for earthquake prediction. It is elaborated that the profile likelihood estimation principle and numerical algorithm of shape parameters and earthquake return level in generalized extreme value distribution. Meanwhile, a model of generalized extreme value distribution was created and was used to analyze the seismic risk of the East Kunlun seismic belt. The results showed that profile likelihood estimation and maximum likelihood estimation generated basically the same effect in point estimation of shape parameters and return level as well as the estimation of confidence interval of earthquake return level within 10 years. However, in the confidence interval estimation of moderate and long interval earthquake return level, the asymmetric confidence interval of return level obtained through the profile likelihood estimation can more accurately express the uncertainty of predicted magnitude of a strong earthquake and more effectively predict the outcome.