Search results for "Point processes"
showing 10 items of 37 documents
Some extensions in space-time LGCP: application to earthquake data
2017
In this paper we aim at studying some extensions of complex space-time models, useful for the description of earthquake data. In particular we want to focus on the Log-Gaussian Cox Process (LGCP, [1]) model estimation approach, with some results on global informal diagnostics. Indeed, in our opinion the use of Cox processes that are natural models for point process phenomena that are environmentally driven could be a new approach for the description of seismic events. These models can be useful in estimating the intensity surface of a spatio-temporal point process, in constructing spatially continuous maps of earthquake risk from spatially discrete data, and in real-time seismic activity su…
Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes
2023
A local version of spatio-temporal log-Gaussian Cox processes is proposed by using Local Indicators of Spatio-Temporal Association (LISTA) functions plugged into the minimum contrast procedure, to obtain space as well as time-varying parameters. The new procedure resorts to the joint minimum contrast fitting method to estimate the set of second-order parameters. This approach has the advantage of being suitable in both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field. Simulation studies to assess the performance of the proposed fitting procedure are presented, and an application to seismic spatio-temporal point pattern…
Minimum contrast for point processes' first-order intensity estimation
2023
In this paper, we exploit some theoretical results, from which we know the expected value of the K-function weighted by the true first-order intensity function of a point pattern. This theoretical result can serve as an estimation method for obtaining the parameter estimates of a specific model, assumed for the data. The only requirement is the knowledge of the first-order intensity function expression, completely avoiding writing the likelihood, which is often complex to deal with in point process models. We illustrate the method through simulation studies for spatio-temporal point processes.
Towards the specification of a self-exciting point process for modelling crimes in Valencia
2023
A number of papers have dealt with the analysis of crime data using self-exciting point process theory after the analogy drawn between aftershock ETAS models and crime rate. With the aim to describe crime events that occurred in Valencia in the last decade, in this paper, we justify the need for a self-exciting point process model through spatial and temporal exploratory analysis.
Comparison between nonparametric and parametric estimate of the conditional intensity function of a seismic space-time point process
2008
A seismic gap can be defined as a segment of an active geologic fault that has not produced seismic events for an unusually long time; gaps are often considered susceptible to future strong earthquakes occurrence and therefore their identification may be useful for predictive purposes. In this paper we try to identify gaps in an area of South Tyrrhenian Sea by comparing the observed seismicity, estimated by nonparametric method, and the theoretical one, described by a particular space-time point process (ETAS model).
Marked Hawkes processes for Twitter data
2022
In this paper, we propose to model retweet event sequences using a marked Hawkes process, which is a self-exciting point process where the occurrence of previous events in time increases the probability of further events. The aim is to analyse Twitter data combining temporal point processes theory and textual analysis. Since each retweet event carries a set of properties, we mark the process by different characteristics drawn from the textual analysis, finding that the tone of the description of the Twitter user is a good predictor of the number of retweets in a single cascade.
Hawkes processes on networks for crime data
2022
Motivated by the analysis of crime data in Bucaramanga (Colombia), we propose a spatio-temporal Hawkes point process model adapted to events living on linear networks. We first consider a non-parametric modelling strategy, for both the background and the triggering components, and then we include a parametric estimation of the background based on covariates, and a non-parametric one of the triggering effects. Our network model outperforms a planar version, improving the fitting of the self-exciting point process model.
Modeling Forest Tree Data Using Sequential Spatial Point Processes
2021
AbstractThe spatial structure of a forest stand is typically modeled by spatial point process models. Motivated by aerial forest inventories and forest dynamics in general, we propose a sequential spatial approach for modeling forest data. Such an approach is better justified than a static point process model in describing the long-term dependence among the spatial location of trees in a forest and the locations of detected trees in aerial forest inventories. Tree size can be used as a surrogate for the unknown tree age when determining the order in which trees have emerged or are observed on an aerial image. Sequential spatial point processes differ from spatial point processes in that the…
Self-exciting point process modelling of crimes on linear networks
2022
Although there are recent developments for the analysis of first and second-order characteristics of point processes on networks, there are very few attempts in introducing models for network data. Motivated by the analysis of crime data in Bucaramanga (Colombia), we propose a spatiotemporal Hawkes point process model adapted to events living on linear networks. We first consider a non-parametric modelling strategy, for which we follow a non-parametric estimation of both the background and the triggering components. Then we consider a semi-parametric version, including a parametric estimation of the background based on covariates, and a non-parametric one of the triggering effects. Our mode…
Second-order diagnostics for space-time point processes with application to seismic events
2008
A diagnostic method for space-time point process is introduced and used to interpret and assess the goodness of fit of particular models to real data such as the seismic ones. The proposed method is founded on the definition of a weighted process and allows to detect second-order features of data, like long-range dependence and fractal behavior, that are not accounted for by the fitted model. Applications to earthquake data are provided. Copyright © 2008 John Wiley & Sons, Ltd.