Stochastic Declustering of Space-Time Earthquake Occurrences

By Jiancang Zhuang, Yosihiko Ogata, David Vere-Jones. 2002

734 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Environmental Engineering, Epidemiology

View Paper: https://www.semanticscholar.org/paper/3c6ee1d5c7c26a5c3c5ce5fb7749d46d75786824

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Citations in the corpus

Prediction (2010, neutral): “These results have been obtained by rigo rous mathematical derivations using probability generating functions: • non-mean field anomalous exponents for the distribution of “ cluster” sizes due to the interplay between cascades of generation and the power laws of productivity and of marks (magnitudes”
Self-Exciting Point Process Modeling of Crime (2011, background): “(7) Assuming model correctness, the probability that event i is a background event, pii, is given by pii = μ(ti, xi, yi) λ(ti, xi, yi) (8) and the probability that event j triggered event i, pji, is given by pji = g(ti − tj, xi − xj, yi − yj) λ(ti, xi, yi) (9) (Zhuang, Ogata, and Vere-Jones 2002).”
Some limit theorems for Hawkes processes and application to financial statistics (2013, background): “From a wider perspective however, a mathematical analysis of the limiting behaviour of Hawkes processes has a relevance beyond finance: these include seismology of course, for which Hawkes processes were originally introduced (see [28] for instance), and in a more prospective way, one could mention ”
Estimation of Space–Time Branching Process Models in Seismology Using an EM–Type Algorithm (2006, methodology): “However, it should be noted that the EM-type algorithm could just as well be combined with a spatial kernel smoothing method as used by Zhuang et al. (2002, 2004, 2005) in order to estimate continuous background intensities.”
Detecting fluid signals in seismicity data through statistical earthquake modeling (2005, methodology): “To begin with, we use the declustering procedure proposed by Zhuang et al. [2002]. The probability that an event i belongs to the background is calculated by the ratio between background rate and the total occurrence rate, l0/l(ti), where l(ti) is calculated according to equation (3).”
Self-exciting point process models of civilian deaths in Iraq (2011, neutral): “The conditional intensity for a Hawkes process is ( Hawkes and Oakes, 1974 ) l m ( ) ( ) t k gt t k t t k = + − ∑ 0 In equation (1), represents the background rate of events, which in most applications is assumed to be constant in time ( Zhuang et al , 2002 ).”
Earthquake clusters in southern California I: Identification and stability (2013, methodology): “The history of seismicity cluster analysis and the existing declustering approaches [e.g., Gardner and Knopoff, 1974; Reasenberg, 1985; Molchan and Dmitrieva, 1992; Dzwinel et al., 2005; Marsan and Lengline, 2008; Zhuang et al., 2002] suggest that the two problems are related.”
Analyzing earthquake clustering features by using stochastic reconstruction (2004, methodology): “Thus we can estimate the background seismicity and the parameters in the clustering structures simultaneously by an iterative approach as outlined in Algorithm A as follows [Zhuang et al., 2002].”
Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data (2011, methodology): “For example, by using the branching property of the Hawkes process [32], the authors in [20] and [18] were able to provide Expectation-Maximization algorithms to”
Space–time ETAS models and an improved extension (2006, methodology): “Furthermore, by fitting least squares to the diagnostic plots, Zhuang et al. (2004) implies that”
Multidimensional Residual Analysis of Point Process Models for Earthquake Occurrences (2003, methodology): “KEY WORDS: Conditional intensity; ETAS model; Seismology; Separability; Spatial–temporal marked point process.”
Second‐order residual analysis of spatiotemporal point processes and applications in model evaluation (2006, methodology): “model (Zhuang et al., 2002, 2004) (a) Set up the initial background seismicity rate; for example, let û.x/=1.”