Search results for "Point Process."

showing 8 items of 98 documents

Space-Time Forecasting of Seismic Events in Chile

2017

The aim of this work is to study the seismicity in Chile using the ETAS (epidemic type aftershock sequences) space‐time approach. The proposed ETAS model is estimated using a semi‐parametric technique taking into account the parametric and nonparametric components corresponding to the triggered and background seismicity, respectively. The model is then used to predict the temporal and spatial intensity of events for some areas of Chile where recent large earthquakes (with magnitude greater than 8.0 M) occurred.

space‐time point processes conditional intensity function ETAS model etasFLP(R package) forecastSpace timeforecsting Chile esrthquakesSettore SECS-S/01 - StatisticaGeologySeismology
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Integreating geological and seismological data in point process models for seismical analysis

2017

Nowadays in the seismic and geological fields, large and complex data sets are available. This information is a valuable source that can be used for improving the seismic hazard assessment of a given region. In particular, the integration of geologic variables into point process models to study seismic pattern is an open research field that has not been fully explored. In this work, we present several open-access datasets (the catalogue of the earthquakes, geological information such as faults, plate boundary and the presence of volcanoes) that are properly treated to describe the seismicity of events occurred in Greece between 2005 and 2014. We use these datasets to fit an advanced spatial…

spatial covariateearthquakegeologica informationearthquake; point process; spatial covariates; geologica information; GIS; faultsfaultspoint proceGIS
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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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Local methods for complex spatio-temporal point processes

2022

spatial statisticsecond-order characteristicspatio temporal point processesummary statisticsSettore SECS-S/01 - Statisticalocal feature
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Joint second-order parameter estimation for spatio-temporal log-Gaussian Cox processes

2018

We propose a new fitting method to estimate the set of second-order parameters for the class of homogeneous spatio-temporal log-Gaussian Cox point processes. With simulations, we show that the proposed minimum contrast procedure, based on the spatio-temporal pair correlation function, provides reliable estimates and we compare the results with the current available methods. Moreover, the proposed method can be used in the case of both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field. We describe earthquake sequences comparing several Cox model specifications.

spatio-temporal pair correlation functionEnvironmental EngineeringGaussianminimum contrast methodnon-separable covariance function010502 geochemistry & geophysics01 natural sciencesPoint processGaussian random fieldSet (abstract data type)010104 statistics & probabilitysymbols.namesakeCorrelation functionEnvironmental Chemistry0101 mathematicsSafety Risk Reliability and Qualityearthquakes0105 earth and related environmental sciencesGeneral Environmental ScienceWater Science and TechnologyParametric statisticsMathematicslog-Gaussian Cox processesEstimation theoryContrast (statistics)symbolsEarthquakes Log-Gaussian Cox processes Minimum contrast method Non-separable covariance function Spatio-temporal pair correlation functionSettore SECS-S/01 - StatisticaAlgorithm
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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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The Homogeneous Poisson Point Process

2008

symbols.namesakeComplete spatial randomnessUniqueness theorem for Poisson's equationCompound Poisson processMathematical analysisDiscrete Poisson equationHomogeneous poisson point processsymbolsFractional Poisson processMathematics
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The Poisson Point Process

2020

Poisson point processes can be used as a cornerstone in the construction of very different stochastic objects such as, for example, infinitely divisible distributions, Markov processes with complex dynamics, objects of stochastic geometry and so forth.

symbols.namesakeCompound Poisson distributionComputer sciencePoisson point processCompound Poisson processsymbolsMarkov processStatistical physicsFractional Poisson processLévy processStochastic geometryPoint process
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