Search results for "Point proce"

Spatial Mark-Recapture Method in the Estimation of Crayfish Population Size

1995

The mark-recapture method is considered for estimation of population size of slowly moving animals like crayfish. The Petersen type estimator for closed population is generalized for situations where recaptures are spatially dependent between the capture sites, and its variance approximation is derived using point processes as models for the population. The method of quadratic forms is suggested to be used as variance estimator. Finally, a trapping design is proposed where onc trap at recapture is replaced by four adjacent traps. A simulation experiment is performed to explain the robusticity of the new trapping design against movements of animals.

Deducing self-interaction in eye movement data using sequential spatial point processes

2016

Eye movement data are outputs of an analyser tracking the gaze when a person is inspecting a scene. These kind of data are of increasing importance in scientific research as well as in applications, e.g. in marketing and man-machine interface planning. Thus the new areas of application call for advanced analysis tools. Our research objective is to suggest statistical modelling of eye movement sequences using sequential spatial point processes, which decomposes the variation in data into structural components having interpretation. We consider three elements of an eye movement sequence: heterogeneity of the target space, contextuality between subsequent movements, and time-dependent behaviou…

Assessing local differences between the spatio-temporal second-order structure of two point patterns occurring on the same linear network

2021

Abstract We introduce Local Indicators of Spatio-Temporal Association (LISTA) functions on linear networks and use them to build a statistical test for local second-order structure. This allows to identify differences in the spatio-temporal clustering behaviour of two point patterns, a point pattern of interest and a background one, both occurring on the same linear network. We assess the performance of the testing procedure for local second-order structure through simulation studies under a variety of scenarios that also account for different generating point processes. We show that the proposed local test is able to correctly identify the spatio-temporal difference in the local second-ord…

Recent applications of point process methods in forestry statistics

2000

Forestry statistics is an important field of applied statistics with a long tradition. Many forestry problems can be solved by means of point processes or marked point processes. There, the "points" are tree locations and the "marks" are tree characteristics such as diameter at breast height or degree of damage by environmental factors. Point pro- cess characteristics are valuable tools for exploratory data analysis in forestry, for describing the variability of forest stands and for under- standing and quantifying ecological relationships. Models of point pro- cesses are also an important basis of modern single-tree modeling, that gives simulation tools for the investigation of forest stru…

Annealed Invariance Principle for Random Walks on Random Graphs Generated by Point Processes in R-d

2016

International audience; We consider simple random walks on random graphs embedded in R-d and generated by point processes such as Delaunay triangulations, Gabriel graphs and the creek-crossing graphs. Under suitable assumptions on the point process, we show an annealed invariance principle for these random walks. These results hold for a large variety of point processes including Poisson point processes, Matern cluster and Matern hardcore processes which have respectively clustering and repulsiveness properties. The proof relies on the use the process of the environment seen from the particle. It allows to reconstruct the original process as an additive functional of a Markovian process und…

Galaxy clustering: a point process

2016

El 'clustering' de galàxies és l'agregació de galàxies en l'universe produida per la força de la gravetat. Les galàxies tendeixen a formar estructures de major tamany tal com 'clusters' o filaments que formen la xarxa còsmica ('Cosmic Web'). Aquesta Estructura a Gran Escala de l'Univers es pot entendre com el resultat de la distribució de galàxies, un procés en el qual totes les galàxies estan subjectes a forces comuns i comparteixen propietats universals. L'anàlisis d'aquesta distribució es pot realitzar amb técniques de processos puntuals, l'estudi de configuracions de punts sobre un marc. En aquesta tesi fem servir aquesta branca de la estadística en tres approximacions diferents: els es…

Cluster priors in the Bayesian modelling of fMRI data

2001

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…

Classification in point patterns on linear networks under clutter

2022

The problem of features detection under present of clutter in point process on linear networks establishes a methodological and computational challenge with multiple kind of applications as traffic accidents among other. Previous works related to the same topical but developed in more simpler geometries tackles the issue of the clutter removal through the distance of nearest-neighbour and show good results with high classification rates. We extend this procedure to the linear networks motivated by the classification of the traffic accidents on the road network of a city. Simulations demonstrate the performance of the method.

A space-time branching process with covariates

2018

The paper proposes a stochastic process that improves the assessment of seismic events in space and time, considering a contagion model (branching process) within a regression-like framework. The proposed approach develops the Forward Likelihood for prediction (FLP) method including covariates in the epidemic component.