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We present an approximate Bayesian inference approach for estimating the intensity of an inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the…

Machine Learning · Statistics 2019-05-06 Christian Donner , Manfred Opper

Intensity estimation is a common problem in statistical analysis of spatial point pattern data. This paper proposes a nonparametric Bayesian method for estimating the spatial point process intensity based on mixture of finite mixture (MFM)…

Methodology · Statistics 2019-07-09 Junxian Geng , Wei Shi , Guanyu Hu

The aim of change-point detection is to identify behavioral shifts within time series data. This article focuses on scenarios where the data is derived from an inhomogeneous Poisson process or a marked Poisson process. We present a…

Methodology · Statistics 2024-11-07 C. Dion-Blanc , D. Hawat , E. Lebarbier , S. Robin

We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…

Methodology · Statistics 2020-03-31 Shota Gugushvili , Frank van der Meulen , Moritz Schauer , Peter Spreij

We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through…

Methodology · Statistics 2021-10-26 Hyotae Kim , Athanasios Kottas

Non-homogeneous Poisson processes are used in a wide range of scientific disciplines, ranging from the environmental sciences to the health sciences. Often, the central object of interest in a point process is the underlying intensity…

Methodology · Statistics 2022-02-11 Tin Lok James Ng , Andrew Zammit-Mangion

This work studies nonparametric Bayesian estimation of the intensity function of an inhomogeneous Poisson point process in the important case where the intensity depends on covariates, based on the observation of a single realisation of the…

Statistics Theory · Mathematics 2025-05-09 Matteo Giordano , Alisa Kirichenko , Judith Rousseau

We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains…

Recent advances in local models for point processes have highlighted the need for flexible methodologies to account for the spatial heterogeneity of external covariates influencing process intensity. In this work, we introduce tessellated…

Methodology · Statistics 2025-04-11 Nicoletta D'Angelo

First-order separability of a spatio-temporal point process plays a fundamental role in the analysis of spatio-temporal point pattern data. While it is often a convenient assumption that simplifies the analysis greatly, existing…

Methodology · Statistics 2021-11-22 Mohammad Ghorbani , Nafiseh Vafaei , Jiří Dvořák , Mari Myllymäki

The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…

Optimization and Control · Mathematics 2011-10-13 Zachary T. Harmany , Roummel F. Marcia , Rebecca M. Willett

This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…

Methodology · Statistics 2022-11-16 Flavio B. Gonçalves , Barbara C. C. Dias

We consider expected risk minimization problems when the range of the estimator is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. To facilitate nonlinear…

Machine Learning · Statistics 2022-05-05 Abhishek Chakraborty , Ketan Rajawat , Alec Koppel

The pair correlation function is a fundamental spatial point process characteristic that, given the intensity function, determines second order moments of the point process. Non-parametric estimation of the pair correlation function is a…

Statistics Theory · Mathematics 2023-04-25 Abdollah Jalilian , Yongtao Guan , Rasmus Waagepetersen

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…

Applications · Statistics 2021-07-19 Lihao Yin , Huiyan Sang

The intensity matching approach for tractable performance evaluation and optimization of cellular networks is introduced. It assumes that the base stations are modeled as points of a Poisson point process and leverages stochastic geometry…

Information Theory · Computer Science 2016-04-12 Marco Di Renzo , Wei Lu , Peng Guan

We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. We exhibit a prior on intensities which both leads to a computationally feasible method and enjoys…

Statistics Theory · Mathematics 2013-11-28 Eduard Belitser , Paulo Serra , Harry van Zanten

This paper considers the problem of adaptive estimation of a non-homogeneous intensity function from the observation of n independent Poisson processes having a common intensity that is randomly shifted for each observed trajectory. We show…

Statistics Theory · Mathematics 2011-05-20 Jérémie Bigot , Sébastien Gadat , Thierry Klein , Clément Marteau

Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity…

Machine Learning · Statistics 2017-06-27 Seth Flaxman , Yee Whye Teh , Dino Sejdinovic

We study minimum contrast estimation for parametric stationary determi-nantal point processes. These processes form a useful class of models for repulsive (or regular, or inhibitive) point patterns and are already applied in numerous…

Statistics Theory · Mathematics 2015-10-15 Christophe Biscio , Frédéric Lavancier