Related papers: Variational approach for spatial point process int…
The availability of large spatial data geocoded at accurate locations has fueled a growing interest in spatial modeling and analysis of point processes. The proposed research is motivated by the intensity estimation problem for large…
Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on…
In spatio-temporal point pattern analysis, one of the main statistical objectives is to estimate the first-order intensity function, i.e., the expected number of points per unit area and unit time. This estimation is usually carried out…
Lasso and Dantzig selector are standard procedures able to perform variable selection and estimation simultaneously. This paper is concerned with extending these procedures to spatial point process intensity estimation. We propose adaptive…
Modelling the first-order intensity function is one of the main aims in point process theory, and it has been approached so far from different perspectives. One appealing model describes the intensity as a function of a spatial covariate.…
In this paper, we revisit the original ideas of Stein and propose an estimator of the intensity parameter of a homogeneous Poisson point process defined in $\R^d$ and observed in a bounded window. The procedure is based on a new general…
This work is concerned with the estimation of the intensity parameter of a stationary determinantal point process. We consider the standard estimator, corresponding to the number of observed points per unit volume and a recently introduced…
This paper proposes a new estimation technique for fitting parametric Gibbs point process models to a spatial point pattern dataset. The technique is a counterpart, for spatial point processes, of the variational estimators for Markov…
In this article, we propose a spectral method for a class of multivariate inhomogeneous spatial point processes, namely the second-order intensity reweighted stationary processes. A key ingredient of our approach is utilizing the asymptotic…
In this paper, we harness a result in point process theory, specifically the expectation of the weighted $K$-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an…
This paper is concerned with a robust estimator of the intensity of a stationary spatial point process. The estimator corresponds to the median of a jittered sample of the number of points, computed from a tessellation of the observation…
In this work, we propose new matrix- and tensor-based methodologies for estimating multivariate intensity functions of inhomogeneous point processes. By viewing multivariate intensity functions as infinite-dimensional matrices or tensors…
The purpose of this paper is to estimate the intensity of some random measure by a piecewise constant function on a finite partition of the underlying measurable space. Given a (possibly large) family of candidate partitions, we build a…
We introduce a broad class of models called semiparametric spatial point process for making inference between spatial point patterns and spatial covariates. These models feature an intensity function with both parametric and nonparametric…
Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial…
Estimation of the intensity of a point process is considered within a nonparametric framework. The intensity measure is unknown and depends on covariates, possibly many more than the observed number of jumps. Only a single trajectory of the…
In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…
A spatial point process can be characterized by an intensity function which predicts the number of events that occur across space. In this paper, we develop a method to infer predictive intensity intervals by learning a spatial model using…
We observe $n$ inhomogeneous Poisson processes with covariates and aim at estimating their intensities. We assume that the intensity of each Poisson process is of the form $s (\cdot, x)$ where $x$ is the covariate and where $s$ is an…
Feature selection procedures for spatial point processes parametric intensity estimation have been recently developed since more and more applications involve a large number of covariates. In this paper, we investigate the setting where the…