The P\'olya sum kernel and Bayes estimation
Probability
2012-05-11 v2 Statistics Theory
Statistics Theory
Abstract
We consider a particular Cox process from a Bayesian viewpoint and show that the Bayes estimator of the intensity measure is the so-called P\'olya sum kernel, which occurred recently in the context of the construction of the so-called Papangelou processes. More precisely, if the prior, the directing measure of the Cox process, is a Poisson-Gamma random measure, then the posterior is again a Poisson-Gamma random measure and the Bayes estimator of the intensity is the P\'olya sum kernel. Moreover, we extend this result to doubly stochastic Poisson-Gamma priors and give conditions under which one can identify the Bayes estimator for the intensity.
Cite
@article{arxiv.1202.4696,
title = {The P\'olya sum kernel and Bayes estimation},
author = {Mathias Rafler},
journal= {arXiv preprint arXiv:1202.4696},
year = {2012}
}