什么时候极端事件的规模越大，预测性越好？
When are Extreme Events the better predictable, the larger they are?
摘要：
我们研究了时间序列中极端事件的可预测性。这项工作的重点是了解在哪些情况下，大事件比小事件更好地预测。因此，我们使用一个简单的预测算法的基础上，识别使用极大似然原则的随机结构。使用接收算子特征曲线作为预测质量的度量，我们发现对事件量级的依赖与潜在随机过程的概率分布函数密切相关。我们评估这种依赖的概率分布函数的分析和数值。如果我们假设使用最优的随机结构来进行预测，我们发现，如果潜在的随机过程具有高斯概率分布函数，则大的增量更好地预测，而如果潜在的概率分布函数具有幂律尾部，则更大的增量更难预测。在指数分布函数的情况下，我们发现没有显着的依赖事件的大小。此外，我们将这些结果与相关数据中的增量预测进行比较，即自由射流的速度增量。自由射流中的速度增量与时间尺度有关，要么是渐近高斯分布，要么是渐近指数分布。自由射流数据内的预测的数值结果是在良好的协议与以前的分析考虑随机数。
英文摘要：
We investigate the predictability of extreme events in time series. The focus of this work is to understand under which circumstances large events are better predictable than smaller events. Therefore we use a simple prediction algorithm based on precursory structures which are identified using the maximum likelihood principle. Using the receiver operator characteristic curve as a measure for the quality of predictions we find that the dependence on the event magnitude is closely linked to the probability distribution function of the underlying stochastic process. We evaluate this dependence on the probability distribution function analytically and numerically. If we assume that the optimal precursory structures are used to make the predictions, we find that large increments are better predictable if the underlying stochastic process has a Gaussian probability distribution function, whereas larger increments are harder to predict if the underlying probability distribution function has a power law tail. In the case of an exponential distribution function we find no significant dependence on the event magnitude. Furthermore we compare these results with predictions of increments in correlated data, namely, velocity increments of a free jet flow. The velocity increments in the free jet flow are in dependence on the time scale either asymptotically Gaussian or asymptotically exponential distributed. The numerical results for predictions within free jet data are in good agreement with the previous analytical considerations for random numbers.
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