Search results for "Point Process"

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.

Gamma kernel intensity estimation in time point processes

2009

Semiparametric estimation of conditional intensity functions for space-time processes

2008

When dealing with data coming from a space time inhomogeneous process, there is often the need of obtaining reliable estimates of the conditional intensity function. According to the field of application, intensity function can be estimated through some assessed parametric model, where parameters are estimated by Maximum Likelihood method. If we are only in an exploratory context or we would like to assess the adequacy of the parametric model, some kind of nonparametric estimation is required. Often, isotropic or anisotropic kernel estimates can be used, e.g. using the Silverman rule for the choice of the windows sizes h (Silverman, 1986). When the purpose of the study is the estimation of …

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.

Determinants of spatial intensity of stop locations on cruise passengers tracking data

2021

This paper aims at analyzing the spatial intensity in the distribution of stop locations of cruise passengers during their visit at the destination through a stochastic point process modelling approach on a linear network. Data collected through the integration of GPS tracking technology and questionnaire-based survey on cruise passengers visiting the city of Palermo are used, to identify the main determinants which characterize their stop locations pattern. The spatial intensity of stop locations is estimated through a Gibbs point process model, taking into account for both individual-related variables, contextual-level information, and for spatial interaction among stop points. The Berman…

Locally weighted spatio-temporal minimum contrast for Log-Gaussian Cox Processes

2022

We propose a local version of the spatio-temporal log-Gaussian Cox processes (LGCPs) employing the Local Indicators of Spatio-Temporal Association (LISTA) functions into the minimum contrast procedure to obtain space as well as time-varying parameters. We resort to the joint minimum contrast method fitting method to estimate the set of second-order parameters for the class of spatio-temporal LGCPs. This approach has the advantage of being usable in the case of both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field (GRF).

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.

Discussion of "modern statistics of spatial point processes"

2007

The paper ‘Modern statistics for spatial point processes' by Jesper Møller and Rasmus P. Waagepetersen is based on a special invited lecture given by the authors at the 21st Nordic Conference on Mathematical Statistics, held at Rebild, Denmark, in June 2006. At the conference, Antti Penttinen and Eva B. Vedel Jensen were invited to discuss the paper. We here present the comments from the two invited discussants and from a number of other scholars, as well as the authors' responses to these comments. Below Figure 1, Figure 2, etc., refer to figures in the paper under discussion, while Figure A, Figure B, etc., refer to figures in the current discussion. All numbered sections and formulas ref…

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…