Related papers: Non-Homogeneous Poisson Process Intensity Modeling…

Current approaches for collision avoidance and space traffic management face many challenges, mainly due to the continuous increase in the number of objects in orbit and the lack of scalable and automated solutions. To avoid catastrophic…

Consider a unit-intensity point process $\Pi$ on the vertex set $V$ of a transitive non-amenable unimodular graph. We study invariant matchings between $\Pi$ and $V$ having small typical matching distances. When $\Pi$ is either a Poisson…

We consider nonparametric Bayesian estimation and prediction for nonhomogeneous Poisson process models with unknown intensity functions. We propose a class of improper priors for intensity functions. Nonparametric Bayesian inference with…

Let $\eta_t$ be a Poisson point process of intensity $t\geq 1$ on some state space $\Y$ and $f$ be a non-negative symmetric function on $\Y^k$ for some $k\geq 1$. Applying $f$ to all $k$-tuples of distinct points of $\eta_t$ generates a…

This paper addresses a detection problem where several spatially distributed sensors independently observe a time-inhomogeneous stochastic process. The task is to decide between two hypotheses regarding the statistics of the observed…

We are interested in estimating the location of what we call "smooth change-point" from $n$ independent observations of an inhomogeneous Poisson process. The smooth change-point is a transition of the intensity function of the process from…

1. Species distribution models (SDM) are tools used to determine environmental features that influence the geographic distribution of species' abundance and have been used to analyze presence-only records. Analysis of presence-only records…

We exploit a suitable moment-based characterization of the mixture of Poisson distribution for developing Bayesian inference for the unknown size of a finite population whose units are subject to multiple occurrences during an enumeration…

We propose to test the homogeneity of a Poisson process observed on a finite interval. In this framework, we first provide lower bounds for the uniform separation rates in $\mathbb{L}^2$ norm over classical Besov bodies and weak Besov…

The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant…

We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity. The alternatives are stationary self-exciting point processes. We…

A non-homogeneous Poisson cluster model is studied, motivated by insurance applications. The Poisson center process which expresses arrival times of claims, triggers off cluster member processes which correspond to number or amount of…

Extracting robust inferences on physical quantities from disk kinematics measured from Doppler-shifted molecular line emission is challenging due to the data's size and complexity. In this paper we develop a flexible linear model of the…

The analysis of panel count data has garnered considerable attention in the literature, leading to the development of multiple statistical techniques. In inferential analysis, most works focus on leveraging estimating equation-based…

We examine optimal matchings or transport between two stationary random measures. It covers allocation from the Lebesgue measure to a point process and matching a point process to a regular (shifted) lattice. The main focus of the article…

An algorithm for the unbiased simulation of continuous max-(resp.\ min-)id stochastic processes is developed. The algorithm only requires the simulation of finite Poisson random measures on the space of continuous functions and avoids the…

In recent years, a number of functional inequalities have been derived for Poisson random measures, with a wide range of applications. In this paper, we prove that such inequalities can be extended to the setting of marked temporal point…

High-dimensional self-exciting point processes have been widely used in many application areas to model discrete event data in which past and current events affect the likelihood of future events. In this paper, we are concerned with…

We present a perfect simulation algorithm for measures that are absolutely continuous with respect to some Poisson process and can be obtained as invariant measures of birth-and-death processes. Examples include area- and…

Define the scaled empirical point process on an independent and identically distributed sequence $\{Y_i: i\le n\}$ as the random point measure with masses at $a_n^{-1} Y_i$. For suitable $a_n$ we obtain the weak limit of these point…