### Abstract

Lingua originale | English |
---|---|

Titolo della pubblicazione ospite | EMS 2019 Program and Book of Abstracts |

Numero di pagine | 1 |

Stato di pubblicazione | Published - 2019 |

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*EMS 2019 Program and Book of Abstracts*

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

Risultato della ricerca: Conference contribution

*EMS 2019 Program and Book of Abstracts.*

}

TY - GEN

T1 - Weighted local second-order statistics for complex spatio-temporal point processes

AU - Siino, Marianna

AU - Adelfio, Giada

PY - 2019

Y1 - 2019

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

M3 - Conference contribution

BT - EMS 2019 Program and Book of Abstracts

ER -