A self‐exciting marked point process model for drought analysis

Li, Xiaoting; Genest, Christian; Jalbert, Jonathan

doi:10.1002/env.2697

Cited by 6 publications

(4 citation statements)

References 33 publications

(41 reference statements)

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“…Hawkes processes or self‐exciting processes, first introduced by Hawkes (1971a, 1971b), are counting processes often used to model the “arrivals” of some events over time, when each arrival increases the probability of subsequent arrivals in its proximity. Typical applications can be found in seismology (Ogata, 1988, 2011; Ogata & Zhuang, 2006; Schoenberg, 2022), capture‐recapture (Altieri et al, 2022; Weller et al, 2018), invasive species (Balderama et al, 2012), droughts (Li et al, 2021), crime (Mohler, 2013; Mohler et al, 2011, 2018), finance (Azizpour et al, 2018; Filimonov & Sornette, 2012; Hawkes, 2018), disease mapping (Chiang et al, 2022; Garetto et al, 2021), wildfires (Peng et al, 2005), and social network analysis (Kobayashi & Lambiotte, 2016; Zhou et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Approximation of Bayesian Hawkes process with inlabru

2023

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Hawkes process are very popular mathematical tools for modeling phenomena exhibiting a self-exciting or self-correcting behavior. Typical examples are earthquakes occurrence, wild-fires, drought, capture-recapture, crime violence, trade exchange, and social network activity. The widespread use of Hawkes process in different fields calls for fast, reproducible, reliable, easy-to-code techniques to implement such models. We offer a technique to perform approximate Bayesian inference of Hawkes process parameters based on the use of the R-package inlabru . The inlabru R-package, in turn, relies on the INLA methodology to approximate the posterior of the parameters. Our Hawkes process approximation is based on a decomposition of the log-likelihood in three parts, which are linearly approximated separately. The linear approximation is performed with respect to the mode of the parameters' posterior distribution, which is determined with an iterative gradient-based method. The approximation of the posterior parameters is therefore deterministic, ensuring full reproducibility of the results. The proposed technique only requires the user to provide the functions to calculate the different parts of the decomposed likelihood, which are internally linearly approximated by the R-package inlabru . We provide a comparison with the bayesianETAS R-package which is based on an MCMC method. The two techniques provide similar results but our approach requires two to ten times less computational time to converge, depending on the amount of data.

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Section: Introductionmentioning

confidence: 99%

Approximation of Bayesian Hawkes process with inlabru

2023

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“…see Blanchet et al, 2018;Evin et al, 2018;Naveau et al, 2016;Taillardat et al, 2019;Taillardat & Mestre, 2020;Tencaliec et al, 2020), to model the river discharges (e.g. see Li et al, 2021), the daily temperature maxima (e.g. see Stein, 2021b), the wind speed (e.g.…”

Section: Introductionmentioning

confidence: 99%

A flexible extended generalized Pareto distribution for tail estimation

Gamet

Jalbert

2022

Environmetrics

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For both financial and environmental applications, tail distributions often correspond to extreme risks and an accurate modeling is mandatory. The peaks-over-threshold model is a classic way to model the exceedances over a high threshold with the generalized Pareto distribution. However, for some applications, the choice of a high threshold is challenging and the asymptotic conditions for using this model are not always satisfied. The class of extended generalized Pareto models can be used in this case. However, the existing extended model have either infinite or null density at the threshold, which is not consistent with tail modeling. In the present article, we propose new extensions of the generalized Pareto distribution for which the density at the threshold is positive and finite. The proposed extensions provide better estimate of the upper tail index for low thresholds than existing models. They are also appropriate for high thresholds because in that case, the extended models simplify to the generalize Pareto model. The performance and flexibility of the models are illustrated with the modeling of temperature exceeding a low threshold and non-zero precipitations recorded in Montreal. For non-zero precipitation, the very low threshold of 0 is used.

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“…The Hawkes point process model (Hawkes, 1971), a type of branching point process model, has been used for a wide variety of applications, including seismology (Adelfio & Chiodi, 2008; Chiodi & Adelfio, 2011; Molyneux et al, 2018; Nichols & Schoenberg, 2014; Ogata, 1998; Siino et al, 2019), invasive species (Balderama et al, 2012), disease epidemics (Meyer et al, 2012), reported crimes (Mohler et al, 2011), drought events (Li et al, 2021), terrorist attacks (Clauset & Woodard, 2013), financial events (Bacry et al 2015). Hawkes models have long been used in seismology to describe the rate of aftershock activity following an earthquake (Ogata, 1988; Ogata, 1998) and have outperformed alternatives for earthquake forecasting (Gordon et al, 2015; Zechar et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Nonparametric estimation of variable productivity Hawkes processes

Schoenberg

2022

Environmetrics

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Hawkes models are frequently used to describe point processes that are clustered spatial‐temporally, and have been used in numerous applications including the study of earthquakes, invasive species, and contagious diseases. An extension of the Hawkes model is considered where the productivity is variable. In particular, the case is explored where each point may have its own productivity and a simple analytic formula is derived for the maximum likelihood estimators of these productivities. This estimator is compared with an empirical estimator and ways are explored of stabilizing both estimators by lower truncating, smoothing, and rescaling the estimates. Properties of the estimators are explored in simulations, and the methods are applied to seismological and epidemic datasets to show and quantify substantial variation in productivity.

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A self‐exciting marked point process model for drought analysis

Cited by 6 publications

References 33 publications

Approximation of Bayesian Hawkes process with inlabru

Approximation of Bayesian Hawkes process with inlabru

A flexible extended generalized Pareto distribution for tail estimation

Nonparametric estimation of variable productivity Hawkes processes

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