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
and I am surprised to find otherwise.
Ben Hough, J., Manjunath Krishnapur, Yuval Peres, and Bálint Virág. 2006. “Determinantal Processes and Independence.” Probability Surveys
3 (0): 206–29.
Eisenbaum, Nathalie, and Haya Kaspi. 2009. “On Permanental Processes.” Stochastic Processes and Their Applications
119 (5): 1401–15.
Lavancier, Frédéric, Jesper Møller, and Ege Rubak. 2015. “Determinantal Point Process Models and Statistical Inference.” Journal of the Royal Statistical Society: Series B (Statistical Methodology)
77 (4): 853–77.
McCullagh, Peter, and Jesper Møller. 2006. “The Permanental Process.” Advances in Applied Probability
38 (4): 873–88.
Møller, Jesper, and Rasmus Waagepetersen. 2017. “Some Recent Developments in Statistics for Spatial Point Patterns.” Annual Review of Statistics and Its Application
4 (1): 317–42.
Walder, Christian J., and Adrian N. Bishop. 2017. “Fast Bayesian Intensity Estimation for the Permanental Process.”
In International Conference on Machine Learning