2020/01/20 by Leigh Shlomovich, Shlomovich, Leigh, Edward A. K. Cohen +6
Biochemistry, Genetics and Molecular Biology · Mathematics · #62M09 #Diffusion and Search Dynamics #FOS: Computer and information sciences #Methodology (stat.ME) #Morphological variations and asymmetry #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2001.07160
openalex publication_date 2020/01/20 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
A key difficulty that arises from real event data is imprecision in the\nrecording of event time-stamps. In many cases, retaining event times with a\nhigh precision is expensive due to the sheer volume of activity. Combined with\npractical limits on the accuracy of measurements, aggregated data is common. In\norder to use point processes to model such event data, tools for handling\nparameter estimation are essential. Here we consider parameter estimation of\nthe Hawkes process, a type of self-exciting point process that has found\napplication in the modeling of financial stock markets, earthquakes and social\nmedia cascades. We develop a novel optimization approach to parameter\nestimation of aggregated Hawkes processes using a Monte Carlo\nExpectation-Maximization (MC-EM) algorithm. Through a detailed simulation\nstudy, we demonstrate that existing methods are capable of producing severely\nbiased and highly variable parameter estimates and that our novel MC-EM method\nsignificantly outperforms them in all studied circumstances. These results\nhighlight the importance of correct handling of aggregated data.\n