Nonparametric Bayesian estimation for multivariate Hawkes processes
研究了多元霍克斯过程参数的非参数贝叶斯估计，推导了后验收敛速度，并通过模拟验证了在神经元功能连接图推断中的应用。
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 $\mathbb{L}_{1}$-metrics for stochastic intensities of the Hawkes process. We then deduce rates for the $\mathbb{L}_{1}$-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. We also present a simulation study to illustrate our results and to study empirically the inference on functional connectivity graphs of neurons