2012/02/21 by Mathias Rafler, Rafler, Mathias
Computer Science · Economics, Econometrics and Finance · Mathematics · #60G55 #60G57 #60G60 #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics #math.PR #math.ST #msc:60G55 #msc:60G57 #msc:60G60 #stat.TH
paper · pdf · doi:10.48550/arxiv.1202.4696
openalex publication_date 2012/02/21 · arxiv created 2012/05/10 · arxiv updated 2012/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a particular Cox process from a Bayesian viewpoint and show that the Bayes estimator of the intensity measure is the so-called Pólya 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 Pólya 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.