Search results for "Point Process."
showing 10 items of 98 documents
An algorithm for earthquakes clustering based on maximum likelihood
2007
In this paper we propose a clustering technique set up to separate and find out the two main components of seismicity: the background seismicity and the triggered one. We suppose that a seismic catalogue is the realization of a non homogeneous space-time Poisson clustered process, with a different parametrization for the intensity function of the Poisson-type component and of the clustered (triggered) component. The method here proposed assigns each earthquake to the cluster of earthquakes, or to the set of independent events, according to the increment to the likelihood function, computed using the conditional intensity function estimated by maximum likelihood methods and iteratively chang…
Detection of cosmic filaments using the Candy model
2004
We propose to apply a marked point process to automatically delineate filaments of the large-scale structure in redshift catalogues. We illustrate the feasibility of the idea on an example of simulated catalogues, describe the procedure, and characterize the results. We find the distribution of the length of the filaments, and suggest how to use this approach to obtain other statistical characteristics of filamentary networks.
Flexible space-time process for seismic data
2009
Point processes are well studied objects in probability theory and a powerful tool in statistics for modelling and analyzing the distribution of real phenomena, such as the seismic one. Point processes can be specified mathematically in several ways, for instance, by considering the joint distributions of the counts of points in arbitrary sets or defining a complete intensity function. The conditional intensity function is a function of the point history and it is itself a stochastic process depending on the past up to time t. In this paper some techniques to estimate the intensity function of space-time point processes are developed, by following semi-parametric approaches and diagnostic m…
Local characteristics of functional marked point processes with applications to seismic data
2022
We present a family of local inhomogeneous mark-weighted summary statistics for general marked point processes. These capture various types of local dependence structures depending on the specified involved weight function. We use them to propose a local random labeling test. This procedure enables us to identify points and thus regions where the random labeling assumption does not hold, for example, when the (functional) marks are spatially dependent. We further present an application to a seismic point pattern with functional marks provided by seismic waveforms. Indeed, despite the relatively long history of point process theory, few approaches to analyzing spatial point patterns where th…
An approach to hypothesis testing based on local indicators of spatio-temporal association
The detection of clustering structure in a point pattern is one of the major focus of attention in spatio-temporal data mining. For instance, statistical tools for clustering detection and identification of events belonging to clusters are welcome in epidemiology and seismology. Local second-order statistics can provide information on how an event relates to nearby events. We extend local indicators of spatial association (known as LISA functions) into the spatio-temporal context (which then will be called LISTA functions). These functions can be used for local tests in the context of case-control spatio-temporal point patterns, and are able to assess in the neighbourhood of each event if t…
Measuring the Rate of Information Exchange in Point-Process Data With Application to Cardiovascular Variability
2022
The amount of information exchanged per unit of time between two dynamic processes is an important concept for the analysis of complex systems. Theoretical formulations and data-efficient estimators have been recently introduced for this quantity, known as the mutual information rate (MIR), allowing its continuous-time computation for event-based data sets measured as realizations of coupled point processes. This work presents the implementation of MIR for point process applications in Network Physiology and cardiovascular variability, which typically feature short and noisy experimental time series. We assess the bias of MIR estimated for uncoupled point processes in the frame of surrogate…
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…