Search results for " point process"

Kernel estimation and display of a five-dimensional conditional intensity function

2018

The aim of this paper is to find a convenient and effective method of displaying some second order properties in a neighbourhood of a selected point of the process. The used techniques are based on very general high-dimensional nonparametric smoothing developed to define a more gen- eral version of the conditional intensity function introduced in earlier earthquake studies by Vere-Jones (1978). 1976) is commonly used for such a purpose in discussing the cumulative behavior of interpoint distances about an initial point. It is defined as the expected number of events falling within a given distance of the initial event, divided by the overall density (rate in 2-dimensions) of the process, sa…

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…

A semi-parametric stochastic generator for bivariate extreme events

2017

The analysis of multiple extreme values aims to describe the stochastic behaviour of observations in the joint upper tail of a distribution function. For instance, being able to simulate multivariate extreme events is convenient for end users who need a large number of random replications of extremes as input of a given complex system to test its sensitivity. The simulation of multivariate extremes is often based on the assumption that the dependence structure, the so-called extremal dependence function, is described by a specific parametric model. We propose a simulation method for sampling bivariate extremes, under the assumption that the extremal dependence function is semiparametric. Th…

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.

Including covariates in a space-time point process with application to seismicity

2020

AbstractThe paper proposes a spatio-temporal process that improves the assessment of events in space and time, considering a contagion model (branching process) within a regression-like framework to take covariates into account. The proposed approach develops the forward likelihood for prediction method for estimating the ETAS model, including covariates in the model specification of the epidemic component. A simulation study is carried out for analysing the misspecification model effect under several scenarios. Also an application to the Italian seismic catalogue is reported, together with the reference to the developed R package.

Gamma kernel intensity estimation in time point processes

2009

An algorithm for earthquakes clustering based on maximum likelihood

2007

In this paper we propose a clustering technique set up to separate and find out the two main components of seismicity: the background seismicity and the triggered one. We suppose that a seismic catalogue is the realization of a non homogeneous space-time Poisson clustered process, with a different parametrization for the intensity function of the Poisson-type component and of the clustered (triggered) component. The method here proposed assigns each earthquake to the cluster of earthquakes, or to the set of independent events, according to the increment to the likelihood function, computed using the conditional intensity function estimated by maximum likelihood methods and iteratively chang…

The Homogeneous Poisson Point Process

2008

Models and methods for space and space-time interactions in complex point processes with applications on earthquakes

Inhomogeneous spatio-temporal point processes on linear networks for visitors’ stops data

2022

We analyse the spatio-temporal distribution of visitors' stops by touristic attractions in Palermo (Italy) using theory of stochastic point processes living on linear networks. We first propose an inhomogeneous Poisson point process model, with a separable parametric spatio-temporal first-order intensity. We account for the spatial interaction among points on the given network, fitting a Gibbs point process model with mixed effects for the purely spatial component. This allows us to study first-order and second-order properties of the point pattern, accounting both for the spatio-temporal clustering and interaction and for the spatio-temporal scale at which they operate. Due to the strong d…