Search results for "Spatio-temporal point patterns"
showing 6 items of 6 documents
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…
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…
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…
Classification of spatio-temporal point pattern in the presence of clutter using K-th nearest neighbour distances
2019
In a point process spatio-temporal framework, we consider the problem of features detection in the presence of clutters. We extend the methodology of Byers and Raftery (1998) to the spatio-temporal context by considering the properties of the K-th nearest-neighbour distances. We make use of the spatio-temporal distance based on the Euclidean norm where the temporal term is properly weighted. We show the form of the probability distributions of such K-th nearest-neighbour distance. A mixture distribution, whose parameters are estimated with an EM algorithm, is used to classify points into clutters or features. We assess the performance of the proposed approach with a simulation study, togeth…
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…
Comparing local structures of spatio-temporal point processes on linear networks
2022
We employ the Local Indicators of Spatio-Temporal Association (LISTA) functions on linear networks 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 illustrate the proposed methodology analysing a traffic-related problem.