Search results for " point process"
showing 10 items of 51 documents
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…
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.
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.
Integreating geological and seismological data in point process models for seismical analysis
2017
Nowadays in the seismic and geological fields, large and complex data sets are available. This information is a valuable source that can be used for improving the seismic hazard assessment of a given region. In particular, the integration of geologic variables into point process models to study seismic pattern is an open research field that has not been fully explored. In this work, we present several open-access datasets (the catalogue of the earthquakes, geological information such as faults, plate boundary and the presence of volcanoes) that are properly treated to describe the seismicity of events occurred in Greece between 2005 and 2014. We use these datasets to fit an advanced spatial…
Models and methods for space and space-time interactions in complex point processes with applications on earthquakes
Local methods for complex spatio-temporal point processes
2022
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…