Related papers: Approximation intensity for pairwise interaction G…
We consider a stationary Poisson hyperplane process with given directional distribution and intensity in $d$-dimensional Euclidean space. Generalizing the zero cell of such a process, we fix a convex body $K$ and consider the intersection…
The Probability Hypothesis Density (PHD) filter, which is used for multi-target tracking based on sensor measurements, relies on the propagation of the first-order moment, or intensity function, of a point process. This algorithm assumes…
We consider an inhomogeneous Poisson process $X$ on $[0,T]$. The intensity function of $X$ is supposed to be strictly positive and smooth on $[0,T]$ except at the point $\theta$, in which it has either a 0-type singularity (tends to 0 like…
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 consider the path approximation of Bessel processes and develop a new and efficient algorithm. This study is based on a recent work by the authors, on the path approximation of the Brownian motion, and on the construction of specific own…
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…
The maximum composite likelihood estimator for parametric models of determinantal point processes (DPPs) is discussed. Since the joint intensities of these point processes are given by determinant of positive definite kernels, we have the…
The challenges posed by complex stochastic models used in computational ecology, biology and genetics have stimulated the development of approximate approaches to statistical inference. Here we focus on Synthetic Likelihood (SL), a…
This paper establishes quantitative limit theorems for two classes of Cox point processes, quantifying their convergence to a Poisson point process (PPP). We employ Stein's method for PPP aproximation, leveraging the generator approach and…
This paper is devoted to the study of the Bayesian-inference approach in the context of estimating the dipole coupling strength in matter-field interactions. In particular, we consider the simplest model of a two-level system interacting…
This work lies at the intersection of Gibbs models and hyperuniform point processes. Classical Gibbs models, whether defined on lattices or in continuous space, provide flexible tools to describe interacting particle systems but are…
Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model…
Posterior inference for Dirichlet process mixture models is analytically intractable and typically relies on Markov chain Monte Carlo methods, which can become computationally prohibitive at moderate to large sample sizes. In this work, we…
A new approach on the joint estimation of partially exchangeable observations is presented by constructing pairwise dependence between $m$ random density functions, each of which is modeled as a mixture of geometric stick breaking…
Our purpose in this paper is to apply the general methodology for model selection based on T-estimators developed in Birg\'{e} [Ann. Inst. H. Poincar\'{e} Probab. Statist. 42 (2006) 273--325] to the particular situation of the estimation of…
We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and…
This exposition explains the basic ideas of Stein's method for Poisson random variable approximation and Poisson process approximation from the point of view of the immigration-death process and Palm theory. The latter approach also enables…
Adjoint field methods are both elegant and efficient for calculating sensitivity information required across a wide range of physics-based inverse problems. Here we provide a unified approach to the derivation of such methods for problems…
We propose a flexible change-point model for inhomogeneous Poisson Processes, which arise naturally from next-generation DNA sequencing, and derive score and generalized likelihood statistics for shifts in intensity functions. We construct…
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…