{"title":"Bayesian forecasting of Italian seismicity using the spatiotemporal RETAS model","authors":"Tom Stindl , Zelong Bi , Clara Grazian","doi":"10.1016/j.csda.2025.108219","DOIUrl":null,"url":null,"abstract":"<div><div>Spatiotemporal Renewal Epidemic Type Aftershock Sequence models are self-exciting point processes that model the occurrence time, epicenter, and magnitude of earthquakes in a geographical region. The arrival rate of earthquakes is formulated as the superposition of a main shock renewal process and homogeneous Poisson processes for the aftershocks, motivated by empirical laws in seismology. Existing methods for model fitting rely on maximizing the log-likelihood by either direct numerical optimization or Expectation Maximization algorithms, both of which can suffer from convergence issues and lack adequate quantification of parameter estimation uncertainty. To address these limitations, a Bayesian approach is employed, with posterior inference carried out using a data augmentation strategy within a Markov chain Monte Carlo framework. The branching structure is treated as a latent variable to improve sampling efficiency, and a purpose-built Hamiltonian Monte Carlo sampler is implemented to update the parameters within the Gibbs sampler. This methodology enables parameter uncertainty to be incorporated into forecasts of seismicity. Estimation and forecasting are demonstrated on simulated catalogs and an earthquake catalog from Italy. <span>R</span> code implementing the methods is provided in the Supplementary Materials.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"212 ","pages":"Article 108219"},"PeriodicalIF":1.5000,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Statistics & Data Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167947325000957","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Spatiotemporal Renewal Epidemic Type Aftershock Sequence models are self-exciting point processes that model the occurrence time, epicenter, and magnitude of earthquakes in a geographical region. The arrival rate of earthquakes is formulated as the superposition of a main shock renewal process and homogeneous Poisson processes for the aftershocks, motivated by empirical laws in seismology. Existing methods for model fitting rely on maximizing the log-likelihood by either direct numerical optimization or Expectation Maximization algorithms, both of which can suffer from convergence issues and lack adequate quantification of parameter estimation uncertainty. To address these limitations, a Bayesian approach is employed, with posterior inference carried out using a data augmentation strategy within a Markov chain Monte Carlo framework. The branching structure is treated as a latent variable to improve sampling efficiency, and a purpose-built Hamiltonian Monte Carlo sampler is implemented to update the parameters within the Gibbs sampler. This methodology enables parameter uncertainty to be incorporated into forecasts of seismicity. Estimation and forecasting are demonstrated on simulated catalogs and an earthquake catalog from Italy. R code implementing the methods is provided in the Supplementary Materials.
期刊介绍:
Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas:
I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article.
II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures.
[...]
III) Special Applications - [...]
IV) Annals of Statistical Data Science [...]