Search results for " point processes"

Financial contagion through space-time point processes

2020

AbstractWe propose to study the dynamics of financial contagion by means of a class of point process models employed in the modeling of seismic contagion. The proposal extends network models, recently introduced to model financial contagion, in a space-time point process perspective. The extension helps to improve the assessment of credit risk of an institution, taking into account contagion spillover effects.

Hybrid kernel estimates of space-time earthquake occurrence rates using the Etas model

2010

The following steps are suggested for smoothing the occurrence patterns in a clustered space–time process, in particular the data from an earthquake catalogue. First, the original data is fitted by a temporal version of the ETAS model, and the occurrence times are transformed by using the cumulative form of the fitted ETAS model. Then the transformed data (transformed times and original locations) is smoothed by a space–time kernel with bandwidth obtained by optimizing a naive likelihood cross-validation. Finally, the estimated intensity for the original data is obtained by back-transforming the estimated intensity for the transformed data. This technique is used to estimate the intensity f…

Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems

2023

AbstractTheoretical and applied cancer studies that use individual-based models (IBMs) have been limited by the lack of a mathematical formulation that enables rigorous analysis of these models. However, spatial cumulant models (SCMs), which have arisen from theoretical ecology, describe population dynamics generated by a specific family of IBMs, namely spatio-temporal point processes (STPPs). SCMs are spatially resolved population models formulated by a system of differential equations that approximate the dynamics of two STPP-generated summary statistics: first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances).We exemplify how SCMs can be used i…

Local Spatio-Temporal Log-Gaussian Cox Processes for seismic data analysis

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. We employ the proposed methodology to analyse real seismic data occurred Greece between 2004 and 2015.

Spatial pattern analysis using hybrid models: an application to the Hellenic seismicity

2016

Earthquakes are one of the most destructive natural disasters and the spatial distribution of their epi- centres generally shows diverse interaction structures at different spatial scales. In this paper, we use a multi-scale point pattern model to describe the main seismicity in the Hellenic area over the last 10 years. We analyze the interaction between events and the relationship with geo- logical information of the study area, using hybrid models as proposed by Baddeley et al. ( 2013 ). In our analysis, we find two competing suitable hybrid models, one with a full parametric structure and the other one based on nonpara- metric kernel estimators for the spatial inhomogeneity.

A multi-scale area-interaction model for spatio-temporal point patterns

2018

Models for fitting spatio-temporal point processes should incorporate spatio-temporal inhomogeneity and allow for different types of interaction between points (clustering or regularity). This paper proposes an extension of the spatial multi-scale area-interaction model to a spatio-temporal framework. This model allows for interaction between points at different spatio-temporal scales and the inclusion of covariates. We fit the proposed model to varicella cases registered during 2013 in Valencia, Spain. The fitted model indicates small scale clustering and regularity for higher spatio-temporal scales.

Selecting the Kth nearest-neighbour for clutter removal in spatial point processes through segmented regression models

2023

We consider the problem of feature detection, in the presence of clutter in spatial point processes. A previous study addresses the issue of the selection of the best nearest neighbour for clutter removal. We outline a simple workflow to automatically estimate the number of nearest neighbours by means of segmented regression models applied to an entropy measure of cluster separation. The method is suitable for a feature with clutter as two superimposed Poisson processes on any twodimensional space, including linear networks. We present simulations to illustrate the method and an application to the problem of seismic fault detection.

Spatio-Temporal Linear Network Point Processes for GPS Data Analysis

This work aims at analyzing the spatio-temporal intensity in the distribution of stop locations of cruise passengers during their visit at the destination. Data are collected through the integration of GPS tracking technology and questionnaire-based survey on a sample of cruise passengers visiting the city of Palermo (Italy), and they are used to identify the main determinants which characterize cruise passengers’ stop locations pattern. The spatio-temporal distribution of visitors' stops is analysed by mean of the theory of stochastic point processes occurring on linear networks, in order to consider the street configuration of the city and the location of the main attractions. First, an i…

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…