Search results for "Point Proce"
showing 10 items of 112 documents
Local LGCP estimation for spatial seismic processes
2020
Using recent results for local composite likelihood for spatial point processes, we show the performance of advanced and flexible statistical models to describe the spatial displacement of earthquake data. Local models described by Baddeley (2017) allow for the possibility of describing both seismic catalogs and sequences. When analysing seismic sequences, the analysis of the small scale variation is the main issue. The interaction among points is taken into account by Log-Gaussian Cox Processes models through the estimation of the parameters of the covariance of the Gaussian Random Field. In their local version these parameters are allowed to vary spatially, and this is a crucial aspect fo…
Advanced spatio-temporal point processes for the Sicily seismicity analysis
2018
Due to the complexity of the generator process of seismic events, we study under several aspects the interaction structure between earthquake events using recently developed spatio-temporal statistical techniques and models. Using these advanced statistical tools, we aim to characterise the global and local scale cluster behaviour of the Easter Sicily seismicity considering the catalogue data since 2006, when the Italian National Seismic Network was upgraded and earthquake location was sensibly improved. Firstly, we characterise the global complex spatiotemporal interaction structure with the space-time ETAS model where background seismicity is estimated non-parametrically, while triggered …
Study of the interaction structure of the East Sicily Seismicity: global and local scale.
2017
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.
Mixed estimation technique in semi-parametric space-time point processes for earthquake description
2013
An estimation approach for the semi-parametric intensity function of a particular space-time point process is introduced. In particular we want to account for the estimation of parametric and nonparametric components simultaneously, applying a forward predictive likelihood to semi-parametric models. For each event, the probability of being a background event or one belonging to a seismic sequence is therefore estimated.