Conjugacy properties of time-evolving Dirichlet and gamma random measures

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• dc.contributor.author Papaspiliopoulos, Omiros
• dc.contributor.author Ruggiero, Matteo
• dc.contributor.author Spanò, Dario
• dc.date.accessioned 2020-06-04T08:22:27Z
• dc.date.available 2020-06-04T08:22:27Z
• dc.date.issued 2016
• dc.description.abstract We extend classic characterisations of posterior distributions under Dirichlet process and gamma random measures priors to a dynamic framework. We consider the problem of learning, from indirect observations, two families of time-dependent processes of interest in Bayesian nonparametrics: the first is a dependent Dirichlet process driven by a Fleming–Viot model, and the data are random samples from the process state at discrete times; the second is a collection of dependent gamma random measures driven by a Dawson–Watanabe model, and the data are collected according to a Poisson point process with intensity given by the process state at discrete times. Both driving processes are diffusions taking values in the space of discrete measures whose support varies with time, and are stationary and reversible with respect to Dirichlet and gamma priors respectively. A common methodology is developed to obtain in closed form the time-marginal posteriors given past and present data. These are shown to belong to classes of finite mixtures of Dirichlet processes and gamma random measures for the two models respectively, yielding conjugacy of these classes to the type of data we consider. We provide explicit results on the parameters of the mixture components and on the mixing weights, which are time-varying and drive the mixtures towards the respective priors in absence of further data. Explicit algorithms are provided to recursively compute the parameters of the mixtures. Our results are based on the projective properties of the signals and on certain duality properties of their projections.en
• dc.description.sponsorship Supported by the MINECO/FEDER via grant MTM2015-67304-P. Supported by the European Research Council (ERC) through StG “N-BNP” 306406.
• dc.format.mimetype application/pdf
• dc.identifier.citation Papaspiliopoulos O, Ruggiero M, Spanò D. Conjugacy properties of time-evolving Dirichlet and gamma random measures. Electron J Statist. 2016;10(2):3452-89. DOI: 10.1214/16-EJS1194
• dc.identifier.doi http://dx.doi.org/10.1214/16-EJS1194
• dc.identifier.issn 1935-7524
• dc.identifier.uri http://hdl.handle.net/10230/44904
• dc.language.iso eng
• dc.publisher The Institute of Mathematical Statistics and the Bernoulli Society
• dc.relation.ispartof Electronic Journal of Statistics. 2016;10(2):3452-89
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/306406
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/MTM2015-67304-P
• dc.rights Copyright for all articles in EJP is CC BY 4.0.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri https://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Bayesian nonparametricsen
• dc.subject.keyword Dawson–Watanabe processen
• dc.subject.keyword Dirichlet processen
• dc.subject.keyword Dualityen
• dc.subject.keyword Fleming–Viot processen
• dc.subject.keyword Gamma random measureen
• dc.title Conjugacy properties of time-evolving Dirichlet and gamma random measuresen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion