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陈峰: Direct Likelihood Evaluation for the Renewal Hawkes Process

时间:2019-12-24来源:

报告时间2019年12月27日(星期五)14:30

报告地点:翡翠科教楼B座1710

:陈峰 高级讲师, 博士生导师

工作单位:新南威尔士大学统计系

举办单位:数学学院

报告人简介

2008年获香港大学统计学博士学位,自2008年至今供职于澳大利亚新南威尔士大学(UNSW Sydney)统计系,现职高级讲师,博士生导师。研究领域包括统计理论与方法、生存分析、应用概率、应用统计、统计计算等,已在相关领域的国际知名期刊发表学术论文30余篇,并培养毕业博士生三名,另有一名在培。现为国际知名统计学期刊Journal of Statistical Planning and Inference编委会成员及副主编。更多信息见个人主页:https://web.maths.unsw.edu.au/~fengchen/  。

报告简介

An interesting extension of the widely applied Hawkes self-exiting point process, the renewal Hawkes (RHawkes) process, was recently proposed by Wheatley, Filimonov, and Sornette, which has the potential to significantly widen the application domains of the self-exciting point processes. However, they claimed that computation of the likelihood of the RHawkes process requires exponential time and therefore is practically impossible. They proposed two expectation–maximization (EM) type algorithms to compute the maximum likelihood estimator (MLE) of the model parameters. Because of the fundamental role of likelihood in statistical inference, a practically feasible method for likelihood evaluation is highly desirable. In this article, we provide an algorithm that evaluates the likelihood of the RHawkes process in quadratic time, a drastic improvement from the exponential time claimed by Wheatley, Filimonov, and Sornette. We demonstrate the superior performance of the resulting MLEs of the model relative to the EM estimators through simulations. We also present a computationally efficient procedure to calculate the Rosenblatt residuals of the process for goodness-of-fit assessment, and a simple yet efficient procedure for future event prediction. The proposed methodologies were applied on real data from seismology and finance.

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