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In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to…

Methodology · Statistics 2019-03-12 Flávio B. Gonçalves , Dani Gamerman

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

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to…

Machine Learning · Computer Science 2024-01-29 Yongsheng Mei , Mahdi Imani , Tian Lan

We study the performance of nonparametric Bayes procedures for one-dimensional diffusions with periodic drift. We improve existing convergence rate results for Gaussian process (GP) priors with fixed hyper parameters. Moreover, we exhibit…

Statistics Theory · Mathematics 2017-06-15 Jan van Waaij , Harry van Zanten

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…

Methodology · Statistics 2024-06-28 Si Cheng , Jon Wakefield , Ali Shojaie

Given a homogeneous Poisson process on ${\mathbb{R}}^d$ with intensity $\lambda$, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that…

Probability · Mathematics 2011-12-09 Alexander E. Holroyd , Russell Lyons , Terry Soo

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

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…

Statistics Theory · Mathematics 2015-07-31 Marianne Clausel , Jean-François Coeurjolly , Jérôme Lelong

Devising optimal operating strategies for a compressor station relies on the knowledge of compressor characteristics. As the compressor characteristics change with time and use, it is necessary to provide accurate models of the…

Computational Engineering, Finance, and Science · Computer Science 2021-11-24 Akhil Ahmed , Marta Zagorowska , Ehecatl Antonio del Rio-Chanona , Mehmet Mercangöz

We introduce a semi-parametric estimator of the Poisson intensity parameter of a spatial stationary Gibbs point process. Under very mild assumptions satisfied by a large class of Gibbs models, we establish its strong consistency and…

Statistics Theory · Mathematics 2013-08-14 Nadia Morsli , Jean-François Coeurjolly

We derive concentration inequalities for maxima of empirical processes associated with Poisson point processes. The proofs are based on a careful application of Ledoux's entropy method. We demonstrate the utility of the obtained…

Probability · Mathematics 2018-07-19 Martin Kroll

This paper considers the posterior contraction of non-parametric Bayesian inference on non-homogeneous Poisson processes. We consider the quality of inference on a rate function $\lambda$, given non-identically distributed realisations,…

Statistics Theory · Mathematics 2019-06-26 James A. Grant , David S. Leslie

Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e. a nonlinear shift along the time axis,…

Methodology · Statistics 2019-09-25 Glenna Schluck , Wei Wu , Anuj Srivastava

We consider a Cox process with Poisson shot noise intensity which has been widely applied in insurance, finance, queue theory, statistic, and many other fields. Cox process is flexible because its intensity depends on not only the time but…

Probability · Mathematics 2018-12-03 Zailei Cheng , Youngsoo Seol

This article addresses the problem of functional supervised classification of Cox process trajectories, whose random intensity is driven by some exogenous random covariable. The classification task is achieved through a regularized convex…

Statistics Theory · Mathematics 2014-10-16 Gérard Biau , Benoît Cadre , Quentin Paris

There is a lack of point process models on linear networks. For an arbitrary linear network, we consider new models for a Cox process with an isotropic pair correlation function obtained in various ways by transforming an isotropic Gaussian…

Statistics Theory · Mathematics 2024-01-17 Jesper Møller , Jakob G. Rasmussen

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

Computation · Statistics 2016-04-18 Andreas Svensson , Arno Solin , Simo Särkkä , Thomas B. Schön

We propose a novel continuous testing framework to test the intensities of Poisson Processes. This framework allows a rigorous definition of the complete testing procedure, from an infinite number of hypothesis to joint error rates. Our…

Methodology · Statistics 2017-05-25 Franck Picard , Patricia Reynaud-Bouret , Etienne Roquain

We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…

Statistics Theory · Mathematics 2014-07-02 Jean-François Coeurjolly , Jesper Møller

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

Machine Learning · Statistics 2020-10-23 Jakob Lindinger , David Reeb , Christoph Lippert , Barbara Rakitsch