Search results for "Point Proce"

Diagnostics for nonparametric estimation in space-time seismic processes

2010

In this paper we propose a nonparametric method, based on locally variable bandwidths kernel estimators, to describe the space-time variation of seismic activity of a region of Southern California. The flexible estimation approach is introduced together with a diagnostic method for space-time point process, based on the interpretation of some second-order statistics, to analyze the dependence structure of observed data and suggest directions for fit improvement. In this paper we review a diagnostic method for space-time point processes based on the interpretation of the transformed version of some second-order statistics. The method is useful to analyze dependence structures of observed dat…

Procesos puntuales como herramienta para el análisis de posibles fuentes de contaminación

2002

El análisis de un patrón puntual engloba una serie de técnicas que permiten estudiar la distribución de un conjunto de eventos ocurridos sobre una región del plano. Este problema surge en epidemiología cuando se investiga una potencial fuente de contaminación ambiental alrededor de la cual se sospecha que surgen casos de una determinada enfermedad. En el presente trabajo, se explica brevemente en qué consiste el análisis de un patrón puntual y se ilustra con una aplicación a la determinación del origen medioambiental y al estudio de las zonas de mayor riesgo de incidencia en un brote de neumonía por Legionella ocurrido entre mediados de septiembre y principios de octubre en la ciudad de Alc…

Non-Periodic Systems with Continuous Diffraction Measures

2015

The present state of mathematical diffraction theory for systems with continuous spectral components is reviewed and extended. We begin with a discussion of various characteristic examples with singular or absolutely continuous diffraction, and then continue with a more general exposition of a systematic approach via stationary stochastic point processes. Here, the intensity measure of the Palm measure takes the role of the autocorrelation measure in the traditional approach. We furthermore introduce a ‘Palm-type’ measure for general complex-valued random measures that are stationary and ergodic, and relate its intensity measure to the autocorrelation measure.

Minimum contrast for point processes' first-order intensity estimation

2023

In this paper, we exploit some theoretical results, from which we know the expected value of the K-function weighted by the true first-order intensity function of a point pattern. This theoretical result can serve as an estimation method for obtaining the parameter estimates of a specific model, assumed for the data. The only requirement is the knowledge of the first-order intensity function expression, completely avoiding writing the likelihood, which is often complex to deal with in point process models. We illustrate the method through simulation studies for spatio-temporal point processes.

Towards the specification of a self-exciting point process for modelling crimes in Valencia

2023

A number of papers have dealt with the analysis of crime data using self-exciting point process theory after the analogy drawn between aftershock ETAS models and crime rate. With the aim to describe crime events that occurred in Valencia in the last decade, in this paper, we justify the need for a self-exciting point process model through spatial and temporal exploratory analysis.

Gamma kernel intensity estimation in time point processes

2009

Semiparametric estimation of conditional intensity functions for space-time processes

2008

When dealing with data coming from a space time inhomogeneous process, there is often the need of obtaining reliable estimates of the conditional intensity function. According to the field of application, intensity function can be estimated through some assessed parametric model, where parameters are estimated by Maximum Likelihood method. If we are only in an exploratory context or we would like to assess the adequacy of the parametric model, some kind of nonparametric estimation is required. Often, isotropic or anisotropic kernel estimates can be used, e.g. using the Silverman rule for the choice of the windows sizes h (Silverman, 1986). When the purpose of the study is the estimation of …

Comparison between nonparametric and parametric estimate of the conditional intensity function of a seismic space-time point process

2008

A seismic gap can be defined as a segment of an active geologic fault that has not produced seismic events for an unusually long time; gaps are often considered susceptible to future strong earthquakes occurrence and therefore their identification may be useful for predictive purposes. In this paper we try to identify gaps in an area of South Tyrrhenian Sea by comparing the observed seismicity, estimated by nonparametric method, and the theoretical one, described by a particular space-time point process (ETAS model).

Marked Hawkes processes for Twitter data

2022

In this paper, we propose to model retweet event sequences using a marked Hawkes process, which is a self-exciting point process where the occurrence of previous events in time increases the probability of further events. The aim is to analyse Twitter data combining temporal point processes theory and textual analysis. Since each retweet event carries a set of properties, we mark the process by different characteristics drawn from the textual analysis, finding that the tone of the description of the Twitter user is a good predictor of the number of retweets in a single cascade.

Determinants of spatial intensity of stop locations on cruise passengers tracking data

2021

This paper aims at analyzing the spatial intensity in the distribution of stop locations of cruise passengers during their visit at the destination through a stochastic point process modelling approach on a linear network. Data collected through the integration of GPS tracking technology and questionnaire-based survey on cruise passengers visiting the city of Palermo are used, to identify the main determinants which characterize their stop locations pattern. The spatial intensity of stop locations is estimated through a Gibbs point process model, taking into account for both individual-related variables, contextual-level information, and for spatial interaction among stop points. The Berman…