2002/05/09 by Lancelot F. James, James, Lancelot F. · 3 citations
Computer Science · Mathematics · #60G09 #60G57 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Bayesian Inference #Stochastic processes and statistical mechanics #math.PR #msc:60G09 #msc:60G57
paper · pdf · doi:10.48550/arxiv.math/0205093
54 pages
arxiv created 2002/05/09 · openalex publication_date 2002/05/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article discusses the usage of a partiton based Fubini calculus for Poisson processes. The approach is an amplification of Bayesian techniques developed in Lo and Weng for gamma/Dirichlet processes. Applications to models are considered which all fall within an inhomogeneous spatial extension of the size biased framework used in Perman, Pitman and Yor. Among some of the results; an explicit partition based calculus is then developed for such models, which also includes a series of important exponential change of measure formula. These results are applied to obtain results for Levy-Cox models, identities related to the two-parameter Poisson-Dirichlet process and other processes, generalisations of the Markov-Krein correspondence, calculus for extended Neutral to the Right processes, among other things.