Search results for "Cox process"

Hierarchical log Gaussian Cox process for regeneration in uneven-aged forests

2021

We propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points x affects another set of points y but not vice versa. We use the model to investigate the effect of large trees to the locations of seedlings. In the model, every point in x has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influence field inside the window. We propose an edge correction to account for this missing data. The par…

Spatio-temporal log-Gaussian Cox processes on earthquake events

2016

This work presents an application of spatio-temporal log-Gaussian Cox processes for the description of earthquake events. To explain the overall spatial trend, spatial geological information in the study area such as faults and volcanoes are introduced in the model. Moreover, an anisotropic specification of the covariance matrix of the Gaussian process is used to improve the explanation of the phenomenon. We apply and compare different models to explain the seismic events occurred in Alaska over the last decades.

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.

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…

Statistical models and inference for spatial point patterns with intensity-dependent marks

2009

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…

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).

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…

On statistical inference for the random set generated Cox process with set-marking.

2007

Cox point process is a process class for hierarchical modelling of systems of non-interacting points in ℝd under environmental heterogeneity which is modelled through a random intensity function. In this work a class of Cox processes is suggested where the random intensity is generated by a random closed set. Such heterogeneity appears for example in forestry where silvicultural treatments like harvesting and site-preparation create geometrical patterns for tree density variation in two different phases. In this paper the second order property, important both in data analysis and in the context of spatial sampling, is derived. The usefulness of the random set generated Cox process is highly…

Recent applications of point process methods in forestry statistics

2000

Forestry statistics is an important field of applied statistics with a long tradition. Many forestry problems can be solved by means of point processes or marked point processes. There, the "points" are tree locations and the "marks" are tree characteristics such as diameter at breast height or degree of damage by environmental factors. Point pro- cess characteristics are valuable tools for exploratory data analysis in forestry, for describing the variability of forest stands and for under- standing and quantifying ecological relationships. Models of point pro- cesses are also an important basis of modern single-tree modeling, that gives simulation tools for the investigation of forest stru…