Hawkes process are very popular mathematical tools for modeling phenomena exhibiting a self-exciting or self-correcting behavior. Typical examples are earthquakes occurrence, wild-fires, drought, capture-recapture, crime violence, trade exchange, and social network activity. The widespread use of Hawkes process in different fields calls for fast, reproducible, reliable, easy-to-code techniques to implement such models. We offer a technique to perform approximate Bayesian inference of Hawkes process parameters based on the use of the R-package inlabru . The inlabru R-package, in turn, relies on the INLA methodology to approximate the posterior of the parameters. Our Hawkes process approximation is based on a decomposition of the log-likelihood in three parts, which are linearly approximated separately. The linear approximation is performed with respect to the mode of the parameters' posterior distribution, which is determined with an iterative gradient-based method. The approximation of the posterior parameters is therefore deterministic, ensuring full reproducibility of the results. The proposed technique only requires the user to provide the functions to calculate the different parts of the decomposed likelihood, which are internally linearly approximated by the R-package inlabru . We provide a comparison with the bayesianETAS R-package which is based on an MCMC method. The two techniques provide similar results but our approach requires two to ten times less computational time to converge, depending on the amount of data.

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使用 inlabru 逼近贝叶斯霍克斯过程

霍克斯过程是非常流行的数学工具，用于对表现出自激励或自校正行为的现象进行建模。典型示例包括地震发生、野火、干旱、夺回、犯罪暴力、贸易交流和社交网络活动。霍克斯过程在不同领域的广泛使用需要快速、可重复、可靠、易于编码的技术来实现此类模型。我们提供了一种基于 R 包inlabru的使用来执行 Hawkes 过程参数的近似贝叶斯推理的技术 。因拉布鲁_ 反过来，R-package 依赖 INLA 方法来近似参数的后验。我们的霍克斯过程近似基于对数似然分解为三个部分，这三个部分分别进行线性近似。线性近似是针对参数后验分布的模式进行的，该模式是通过基于迭代梯度的方法确定的。因此，后验参数的近似是确定性的，确保结果的完全可重复性。所提出的技术仅要求用户提供计算分解似然的不同部分的函数，这些函数由 R 包inlabru内部线性近似 。我们提供与贝叶斯ETAS的比较基于 MCMC 方法的 R 包。这两种技术提供了相似的结果，但我们的方法收敛所需的计算时间减少了两到十倍，具体取决于数据量。