Search results for "Point Proce"

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.

Some properties of local weighted second-order statistics for spatio-temporal point processes

2019

Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data into residuals as a result of a thinning or a rescaling procedure. We alternatively consider here second-order statistics coming from weighted measures. Motivated by Adelfio and Schoenberg (Ann Inst Stat Math 61(4):929–948, 2009) for the temporal and spatial cases, we consider an extension to the spatio-temporal context in addition to focussing on local characteristics. In particular, our proposed method assesses goodness-of-fit of spatio-temporal models by using local weighted second-order statistics, computed after weighting the contribution of each observed point by the…

Local inhomogeneous weighted summary statistics for marked point processes

2023

We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture different kinds of local dependence structures. We first derive some basic properties and show how these new statistical tools can be used to construct most existing summary statistics for (marked) point processes. We then propose a local test of random labelling. This procedure allows us to identify points, and consequently regions, where the random labelling assumption does not hold, e.g.~when the (functional) marks are spatially dependent. Through a simulatio…

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.

Source Detection in an Outbreak of Legionnaire’s Disease

2006

Spatial statistics have broadly been applied, developed and demanded from the field of epidemiology. The point process theory is an appropriate framework to analyse the spatial variation of risk of disease from information at individual level.

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…

Nonparametric clustering of seismic events

2006

In this paper we propose a clustering technique, based on the maximization of the likelihood function defined from the generalization of a model for seismic activity (ETAS model, (Ogata (1988))), iteratively changing the partitioning of the events. In this context it is useful to apply models requiring the distinction between independent events (i.e. the background seismicity) and strongly correlated ones. This technique develops nonparametric estimation methods of the point process intensity function. To evaluate the goodness of fit of the model, from which the clustering method is implemented, residuals process analysis is used.

Local test of random labelling for functional marked point processes

2022

We introduce the local t-weighted marked nth-order inhomogeneous K-function, in a Functional Marked Point Processes framework. We employ the proposed summary statistics to run a local test of random labelling, useful to identify points, and consequently regions, where this assumption does not hold, i.e. the functional marks are spatially dependent.

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…