Optimality of Poisson processes intensity learning with Gaussian\n processes

2014/09/17 by Alisa Kirichenko, Kirichenko, Alisa, Harry van Zanten +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Point processes and geometric inequalities #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1409.5103

openalex publication_date 2014/09/17 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

In this paper we provide theoretical support for the so-called "Sigmoidal\nGaussian Cox Process" approach to learning the intensity of an inhomogeneous\nPoisson process on a d-dimensional domain. This method was proposed by Adams,\nMurray and MacKay (ICML, 2009), who developed a tractable computational\napproach and showed in simulation and real data experiments that it can work\nquite satisfactorily. The results presented in the present paper provide\ntheoretical underpinning of the method. In particular, we show how to tune the\npriors on the hyper parameters of the model in order for the procedure to\nautomatically adapt to the degree of smoothness of the unknown intensity and to\nachieve optimal convergence rates.\n

Citations

• A note on non-parametric Bayesian estimation for Poisson point processes

Cited by

• A nonparametric Bayesian analysis of independent and identically distributed observations of covariate-driven Poisson processes

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