Fast Bayesian Intensity Estimation for the Permanental Process

Abstract

The Cox process is a stochastic process which generalises the Poisson process by letting the underlying intensity function itself be a stochastic process. In this paper we present a fast Bayesian inference scheme for the permanental process, a Cox process under which the square root of the intensity is a Gaussian process. In particular we exploit connections with reproducing kernel Hilbert spaces, to derive efficient approximate Bayesian inference algorithms based on the Laplace approximation to the predictive distribution and marginal likelihood. We obtain a simple algorithm which we apply to toy and real-world problems, obtaining orders of magnitude speed improvements over previous work.

Cited by in corpus (8)

• Instrumental Variable Regression via Kernel Maximum Moment Loss
• Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes
• All your loss are belong to Bayes
• Structured Variational Inference in Continuous Cox Process Models
• Efficient Non-parametric Bayesian Hawkes Processes
• Sensing Cox Processes via Posterior Sampling and Positive Bases
• Quantile Propagation for Wasserstein-Approximate Gaussian Processes
• Spatio-temporal extreme event modeling of terror insurgencies