Search results for "Point processes"

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.

Local indicators of spatio-temporal association on linear networks

In this work, we extend the Local Indicators of Spatio-Temporal Association (LISTA) functions (Siino et al. 2018) to the non-Euclidean space of linear networks. We introduce the local version of some inhomogeneous second-order statistics for spatio-temporal point processes on linear networks (Morandi and Mateu, 2019), namely the K-function and the pair correlation function. Following the work of Adelfio et al. (2019) for the Euclidean case, we employ the proposed LISTA functions to assess the goodness-of-fit of different spatio-temporal models fitted to point patterns occurring on linear networks. Indeed, the peculiar lack of homogeneity in a network discourages the usage of traditional spa…

Statistical inference for eye movement sequences using spatial and spatio-temporal point processes

2017

Eye tracking is a widely used method for recording eye movements, which are important indicators of ongoing cognitive processes during the viewing of a target stimulus. Despite the variety of applications, the analyses of eye movement data have been lacking of methods that could take both the spatial and temporal information into account. So far, most of the analyses are based on strongly aggregated measures, because eye movement data are considered to be complex due to their richness and large variation between and within the individuals. Therefore, the eye movement methodology needs new statistical tools in order to take full advantage of the data. This dissertation is among the first stud…

Nonparametric intensity estimation in space-time point processes and application to seismological problems

2008

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.

Models and methods for space and space-time interactions in complex point processes with applications on earthquakes

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…