A comprehensive study on methodologies of statistical modeling and inference for Hawks-type point process and applications

2022 Fiscal Year Final Research Report

• Project/Area Number: 19H04073
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 60030:Statistical science-related
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Zhuang Jiancang 統計数理研究所, モデリング研究系, 准教授 (70465920)
• Project Period (FY): 2019-04-01 – 2022-03-31
• Keywords: Hawkes 過程 / ETASモデル / フィルタリング / 地震活動 / 確率再構築法 / 更新Hawkes過程

Outline of Final Research Achievements

Focusing on the developments of the common needs related to Hawkes process,this project has developed and implemented likelihood ratios based on filtering techniques for statistical inference of renewal Hawkes processes, in both closed form and MCMC algorithms. In seismicity application, we extended the space-time ETAS model to incorporate with focal mechanisms, where the response function for focal mechanisms is estimated nonparametrically by using the stochastic reconstruction method. This model is applied to the Hi-net earthquake catalog. The critical theory of extreme events for the generalized ETAS model and its implications for the study of foreshocks and earthquake swarms are summarized and clarified. Furthermore, we have implemented a spherical version of the ETAS model and released the software. The new version is useful for analyzing global seismicity or seismicity in high-altitude region.

Free Research Field

統計科学

Academic Significance and Societal Importance of the Research Achievements

Hawkes 過程は，外的な原因による影響と過去の事象によって誘発・励起される構造によって確率ルールに従って，将来の事象の発生に影響を及ぼす効果を表現するのに向いている。このモデルは事象間の集中化効果（正の相互作用）や潜在的な因果関係を解析するために役立つ線形の基本的なモデルと認識されるようになった。本プロジェクトはHawkes 型点過程の統計モデルを一般的かつ柔軟に様々なアプリケーション分野でのモデリング，診断分析，予測のための準備ツールに資し、予測・検証システム構築と迅速な推定の一般的フレームワークを提供した。