# Permanental point processes

December 4, 2019 — December 4, 2019

linear algebra

Monte Carlo

point processes

Placeholder notes for a type of point process, with which I am unfamiliar, but about which I am incidentally curious.

This is, AFAICT, a point process whose intensity is a squared Gaussian process. The term *permanental* is because the matrix permanent arises somewhere in the model of this process although I know not where (Walder and Bishop 2017). From some incidental comments at a seminar I presumed the permanental process was actually a Gibbs point process (i.e. determined by interactions between points not a latent process) like its determinantal cousin and I am surprised to find otherwise.

## 1 References

Ben Hough, Krishnapur, Peres, et al. 2006. “Determinantal Processes and Independence.”

*Probability Surveys*.
Eisenbaum, and Kaspi. 2009. “On Permanental Processes.”

*Stochastic Processes and Their Applications*.
Lavancier, Møller, and Rubak. 2015. “Determinantal Point Process Models and Statistical Inference.”

*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*.
McCullagh, and Møller. 2006. “The Permanental Process.”

*Advances in Applied Probability*.
Møller, and Waagepetersen. 2017. “Some Recent Developments in Statistics for Spatial Point Patterns.”

*Annual Review of Statistics and Its Application*.
Walder, and Bishop. 2017. “Fast Bayesian Intensity Estimation for the Permanental Process.” In

*International Conference on Machine Learning*.