Search results for "Point Proce"

Some extensions in space-time LGCP: application to earthquake data

2017

In this paper we aim at studying some extensions of complex space-time models, useful for the description of earthquake data. In particular we want to focus on the Log-Gaussian Cox Process (LGCP, [1]) model estimation approach, with some results on global informal diagnostics. Indeed, in our opinion the use of Cox processes that are natural models for point process phenomena that are environmentally driven could be a new approach for the description of seismic events. These models can be useful in estimating the intensity surface of a spatio-temporal point process, in constructing spatially continuous maps of earthquake risk from spatially discrete data, and in real-time seismic activity su…

Statistical models and inference for spatial point patterns with intensity-dependent marks

2009

Finite Point Processes

2008

Stationary Marked Point Processes

2008

Fitting and Testing Point Process Models

2008

Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes

2023

A local version of spatio-temporal log-Gaussian Cox processes is proposed by using Local Indicators of Spatio-Temporal Association (LISTA) functions plugged into the minimum contrast procedure, to obtain space as well as time-varying parameters. The new procedure resorts to the joint minimum contrast fitting method to estimate the set of second-order parameters. This approach has the advantage of being suitable in both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field. Simulation studies to assess the performance of the proposed fitting procedure are presented, and an application to seismic spatio-temporal point pattern…

Kernel intensity for space-time point processes with application to seismological problems

2010

Dealing with data coming from a space-time inhomogeneous process, there is often the need of semi-parametric estimates of the conditional intensity function; isotropic or anisotropic multivariate kernel estimates can be used, with windows sizes h. The properties of the intensities estimated with this choice of h are not always good for specific fields of application; we could try to choose h in order to have good predictive properties of the estimated intensity function. Since a direct ML approach cannot be followed, we propose an estimation procedure, computationally intensive, based on the subsequent increments of likelihood obtained adding an observation at time. The first results obtain…

Comparing estimators of the galaxy correlation function

1999

We present a systematic comparison of some usual estimators of the 2--point correlation function, some of them currently used in Cosmology, others extensively employed in the field of the statistical analysis of point processes. At small scales, it is known that the correlation function follows reasonably well a power--law expression $\xi(r) \propto r^{-\gamma}$. The accurate determination of the exponent $\gamma$ (the order of the pole) depends on the estimator used for $\xi(r)$; on the other hand, its behavior at large scale gives information on a possible trend to homogeneity. We study the concept, the possible bias, the dependence on random samples and the errors of each estimator. Erro…

Statistics of Galaxy Clustering

2006

In this introductory talk we will establish connections between the statistical analysis of galaxy clustering in cosmology and recent work in mainstream spatial statistics. The lecture will review the methods of spatial statistics used by both sets of scholars, having in mind the cross-fertilizing purpose of the meeting series. Special topics will be: description of the galaxy samples, selection effects and biases, correlation functions, nearest neighbor distances, void probability functions, Fourier analysis, and structure statistics.

Space-time Point Processes semi-parametric estimation with predictive measure information

2014

In this paper, we provide a method to estimate the space-time intensity of a branching-type point process by mixing nonparametric and parametric approaches. The method accounts simultaneously for the estimation of the different model components, applying a forward predictive likelihood estimation approach to semi-parametric models.