This paper studies nonparametric estimation of parameters of multivariate Hawkes processes. We consider the Bayesian setting and derive posterior concentration rates. First rates are derived for L1-metrics for stochastic intensities of the Hawkes process. We then deduce rates for the L1-norm of interactions functions of the process. Our results are exemplified by using priors based on piecewise constant functions, with regular or random partitions and priors based on mixtures of Betas distributions. Numerical illustrations are then proposed with in mind applications for inferring functional connec-tivity graphs of neurons.

中文翻译：

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多元霍克斯过程的非参数贝叶斯估计

本文研究了多元霍克斯过程参数的非参数估计。我们考虑贝叶斯设置并得出后验集中率。为霍克斯过程的随机强度的 L1 度量推导出第一速率。然后我们推导出过程的交互函数的 L1 范数的比率。我们的结果通过使用基于分段常数函数的先验、规则或随机分区和基于 Betas 分布混合的先验来举例说明。然后提出了数值说明，考虑到推断神经元功能连接图的应用。