Search results for "spatio-temporal point proce"

showing 5 items of 15 documents

Self-exciting point process modelling of crimes on linear networks

2022

Although there are recent developments for the analysis of first and second-order characteristics of point processes on networks, there are very few attempts in introducing models for network data. Motivated by the analysis of crime data in Bucaramanga (Colombia), we propose a spatiotemporal Hawkes point process model adapted to events living on linear networks. We first consider a non-parametric modelling strategy, for which we follow a non-parametric estimation of both the background and the triggering components. Then we consider a semi-parametric version, including a parametric estimation of the background based on covariates, and a non-parametric one of the triggering effects. Our mode…

Statistics and Probability22/3 OA procedureHawkes processeCovariatecrime datacovariatesself-exciting point processesSelf-exciting point processeSpatio-temporal point processesITC-ISI-JOURNAL-ARTICLELinear networklinear networksspatio-temporal point processesCrime dataStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaHawkes processesStatistical modelling
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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…

Statistics and ProbabilityLog-Gaussian Cox processeSpatio-temporal point processesIntensity estimationGlobal Positioning SystemModeling and SimulationGibbs point processeLinear networkStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaThe Annals of Applied Statistics
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Community detection of seismic point processes

2022

In this paper, we combine robin and Local Indicators of Spatio-Temporal Association (LISTA) functions. robin is an R package to assess the robustness of the community structure of a network found by one or more methods to give indications about their reliability. We use it to propose a classification algorithm of events in a spatio-temporal point pattern, by means of the local second-order characteristics and the community detection procedure in network analysis. We demonstrate the proposed procedure on a real data analysis on seismic data.

network analysis community detection algorithm second-order characteristics spatio-temporal point processes statistical validation earthquakesSettore SECS-S/01 - Statistica
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Models and methods for space and space-time interactions in complex point processes with applications on earthquakes

spatial covariatespatial point processeearthquakes; hybrids of Gibbs point processes; spatial covariates; spatial point processes; hypothesis testing; local indicators of spatio-temporal association; permutation-based tests; second-order product density function; log-Gaussian Cox process; spatial anisotropy; spatio-temporal point process; clustering detectionlog-Gaussian Cox proceearthquakehybrids of Gibbs point processehypothesis testinglocal indicators of spatio-temporal associationpermutation-based testspatial anisotropysecond-order product density functionspatio-temporal point proceSettore SECS-S/01 - Statisticaclustering detection
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Weighted local second-order statistics for complex spatio-temporal point processes

2019

Spatial, temporal, and spatio-temporal point processes, and in particular Poisson processes, are stochastic processes that are largely used to describe and model the distribution of a wealth of real phenomena. When a model is fitted to a set of random points, observed in a given multidimensional space, diagnostic measures are necessary to assess the goodness-of-fit and to evaluate the ability of that model to describe the random point pattern behaviour. The main problem when dealing with residual analysis for point processes is to find a correct definition of residuals. Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data in…

spatio-temporal point processes diagnostics K-function weighted second-order statistics
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