Probabilistic Enhancement of the Failure Forecast Method Using a Stochastic Differential Equation and Application to Volcanic Eruption Forecasts
Probabilistic Enhancement of the Failure Forecast Method Using a Stochastic Differential Equation and Application to Volcanic Eruption Forecasts
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DOI：
10.3389/feart.2019.00135
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发表时间：
2019-07-03
影响因子：
2.9
通讯作者：
Voight, Barry
中科院分区：
文献类型：
--
作者：
Bevilacqua, Andrea;Pitman, Eric Bruce;Voight, Barry
我们介绍了一个双随机方法进行材料失效理论为基础的预测火山爆发。该方法增强了著名的失败预测方法方程，引入了一个新的提法类似于赫尔-怀特模型在金融数学。特别地，我们在原方程中加入了随机噪声项，并系统地描述了不确定性。该模型是一个具有平均回复路径的随机微分方程，其中传统的常微分方程定义了平均解。我们的实现允许模型从经典的解决方案，包括在估计的不确定性，使游览。双随机公式特别强大，因为它提供了一个完整的后验概率分布，允许用户确定具有指定置信度的最坏情况。我们将新方法应用于历史数据集的非线性信号，在广泛的可能值的凸性的解决方案和散射量的观察。结果表明，增加预测技巧的双随机制定的方程相比，统计回归。
We introduce a doubly stochastic method for performing material failure theory based forecasts of volcanic eruptions. The method enhances the well known Failure Forecast Method equation, introducing a new formulation similar to the Hull-White model in financial mathematics. In particular, we incorporate a stochastic noise term in the original equation, and systematically characterize the uncertainty. The model is a stochastic differential equation with mean reverting paths, where the traditional ordinary differential equation defines the mean solution. Our implementation allows the model to make excursions from the classical solutions, by including uncertainty in the estimation. The doubly stochastic formulation is particularly powerful, in that it provides a complete posterior probability distribution, allowing users to determine a worst case scenario with a specified level of confidence. We apply the new method on historical datasets of precursory signals, across a wide range of possible values of convexity in the solutions and amounts of scattering in the observations. The results show the increased forecasting skill of the doubly stochastic formulation of the equations if compared to statistical regression.