Weighted local second-order statistics for complex spatio-temporal point processes

Risultato della ricerca: Conference contribution

Abstract

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 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 (2010) for the spatial case, we consider here an extension to the spatio-temporal context in addition to focussing on local characteristics.Then, rather than using global characteristics, we introduce local tools, considering individual contributions of a global estimator as a measure of clustering. Generally, the individual contributions to a global statistic can be used to identify outlying components measuring the influence of each contribution to the global statistic.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 inverse of the conditional intensity function that identifies the process.Weighted second-order statistics directly apply to data without assuming homogeneity nor transforming the data into residuals, eliminating thus the sampling variability due to the use of a transforming procedure. We provide some characterisations and show a number of simulation studies.
Lingua originaleEnglish
Titolo della pubblicazione ospiteEMS 2019 Program and Book of Abstracts
Numero di pagine1
Stato di pubblicazionePublished - 2019

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Spatio-temporal Process
Point Process
Order Statistics
Goodness of fit
Statistic
Diagnostics
Residual Analysis
Spatio-temporal Model
Intensity Function
Thinning
Rescaling
Poisson process
Homogeneity
Weighting
Stochastic Processes
Simulation Study
Clustering
Model
Estimator
Necessary

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Weighted local second-order statistics for complex spatio-temporal point processes. / Siino, Marianna; Adelfio, Giada.

EMS 2019 Program and Book of Abstracts. 2019.

Risultato della ricerca: Conference contribution

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AU - Adelfio, Giada

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N2 - 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 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 (2010) for the spatial case, we consider here an extension to the spatio-temporal context in addition to focussing on local characteristics.Then, rather than using global characteristics, we introduce local tools, considering individual contributions of a global estimator as a measure of clustering. Generally, the individual contributions to a global statistic can be used to identify outlying components measuring the influence of each contribution to the global statistic.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 inverse of the conditional intensity function that identifies the process.Weighted second-order statistics directly apply to data without assuming homogeneity nor transforming the data into residuals, eliminating thus the sampling variability due to the use of a transforming procedure. We provide some characterisations and show a number of simulation studies.

AB - 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 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 (2010) for the spatial case, we consider here an extension to the spatio-temporal context in addition to focussing on local characteristics.Then, rather than using global characteristics, we introduce local tools, considering individual contributions of a global estimator as a measure of clustering. Generally, the individual contributions to a global statistic can be used to identify outlying components measuring the influence of each contribution to the global statistic.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 inverse of the conditional intensity function that identifies the process.Weighted second-order statistics directly apply to data without assuming homogeneity nor transforming the data into residuals, eliminating thus the sampling variability due to the use of a transforming procedure. We provide some characterisations and show a number of simulation studies.

UR - http://hdl.handle.net/10447/371368

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