Search results for "Second-order characteristic"

showing 10 items of 11 documents

Minimum contrast for point processes' first-order intensity estimation

2023

In this paper, we exploit some theoretical results, from which we know the expected value of the K-function weighted by the true first-order intensity function of a point pattern. This theoretical result can serve as an estimation method for obtaining the parameter estimates of a specific model, assumed for the data. The only requirement is the knowledge of the first-order intensity function expression, completely avoiding writing the likelihood, which is often complex to deal with in point process models. We illustrate the method through simulation studies for spatio-temporal point processes.

Second-order characteristics Spatial statistics Spatio-temporal point processes Local models Minimum contrastSettore SECS-S/01 - Statistica
researchProduct

Some properties and applications of local second-order characteristics for spatio-temporal point processes on networks

2021

Point processes on linear networks are increasingly being considered to analyse events occurring on particular network-based structures. In this work, we extend Local Indicators of Spatio-Temporal Association (LISTA) functions to the non-Euclidean space of linear networks, allowing to obtain information on how events relate to nearby events. In particular, we propose the local version of two inhomogeneous second-order statistics for spatio-temporal point processes on linear networks, the K- and the pair correlation functions. We also show that these LISTA functions are useful for diagnostics of models specified on the networks, and can be helpful to assess the goodness-of-fit of different s…

Linear networks Local properties Residual analysis Second-order characteristics Spatio-temporal point patternsSettore SECS-S/01 - Statistica
researchProduct

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.

Earthquakes Second-order characteristics Spatio-temporal point processes Local models Log-Gaussian Cox Processes Minimum contrastSettore SECS-S/01 - Statistica
researchProduct

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…

Environmental Engineeringsecond-order characteristics010504 meteorology & atmospheric sciencesComputer science0208 environmental biotechnologyresidual analysisInverseComputational intelligence02 engineering and technology01 natural sciencesPoint processSecond order statisticslocal propertiesEnvironmental ChemistryApplied mathematicsSafety Risk Reliability and Quality0105 earth and related environmental sciencesGeneral Environmental ScienceWater Science and TechnologyHomogeneity (statistics)Intensity function020801 environmental engineeringWeightingK-functionspatio-temporal point patternsSettore SECS-S/01 - StatisticaK-function Local properties Residual analysis Second-order characteristics Spatio-temporal point patternsStochastic Environmental Research and Risk Assessment
researchProduct

Local inhomogeneous second-order characteristics for spatio-temporal point processes occurring on linear networks

2022

AbstractPoint processes on linear networks are increasingly being considered to analyse events occurring on particular network-based structures. In this paper, we extend Local Indicators of Spatio-Temporal Association (LISTA) functions to the non-Euclidean space of linear networks, allowing to obtain information on how events relate to nearby events. In particular, we propose the local version of two inhomogeneous second-order statistics for spatio-temporal point processes on linear networks, the K- and the pair correlation functions. We put particular emphasis on the local K-functions, deriving come theoretical results which enable us to show that these LISTA functions are useful for diagn…

Statistics and ProbabilityLocal Indicators of Spatio-Temporal Associationlocal propertiessecond-order characteristicsresidual analysislinear networksspatio-temporal point patternsStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaLinear networks Local Indicators of Spatio-temporal Association Local properties Residual analysis Second-order characteristics Spatio-temporal point patterns
researchProduct

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).

Spatio-temporal point processeSecond-order characteristicsLog-Gaussian Cox ProcesseLocal modelSettore SECS-S/01 - StatisticaMinimum contrast
researchProduct

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…

Methodology (stat.ME)FOS: Computer and information sciencesLocal models log-Gaussian Cox processes Minimum contrast Second-order characteristics Spatio-temporal point processesStatistics and ProbabilityComputational MathematicsComputational Theory and MathematicsApplied MathematicsSettore SECS-S/01 - StatisticaStatistics - ComputationStatistics - MethodologyComputation (stat.CO)Computational Statistics & Data Analysis
researchProduct

Assessing local differences between the spatio-temporal second-order structure of two point patterns occurring on the same linear network

2021

Abstract We introduce Local Indicators of Spatio-Temporal Association (LISTA) functions on linear networks and use them to build a statistical test for local second-order structure. This allows to identify differences in the spatio-temporal clustering behaviour of two point patterns, a point pattern of interest and a background one, both occurring on the same linear network. We assess the performance of the testing procedure for local second-order structure through simulation studies under a variety of scenarios that also account for different generating point processes. We show that the proposed local test is able to correctly identify the spatio-temporal difference in the local second-ord…

Statistics and Probabilitysecond-order characteristicsComputer scienceAssociation (object-oriented programming)Spatio-temporal point patternsStructure (category theory)Management Monitoring Policy and LawPoint processLocal propertielocal propertieshypothesis testinglocal indicators of spatio-temporal associationLinear networkPoint (geometry)Computers in Earth SciencesCluster analysisStatistical hypothesis testingbusiness.industrySecond-order characteristicPattern recognitionPower (physics)Linear networkHypothesis testingLocal Indicators of Spatio-Temporal Associationlinear networksspatio-temporal point patternsArtificial intelligencebusinessSettore SECS-S/01 - Statistica
researchProduct

Local methods for complex spatio-temporal point processes

2022

spatial statisticsecond-order characteristicspatio temporal point processesummary statisticsSettore SECS-S/01 - Statisticalocal feature
researchProduct

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
researchProduct