A class of dependent Dirichlet processes via latent multinomial processes. Issue 5 (3rd September 2021)

• Record Type: Journal Article
• Authors: Nieto-Barajas, Luis E.
• Is Part Of: Statistics. Volume 55:Issue 5(2021)
• Page Start: 1169
• Page End: 1179
• Publication Date: 2021-09-03
• Subjects: Bayesian nonparametrics -- generalized Pólya urn -- moving average process -- spatio-temporal process -- stationary process; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2021.1991348
• Languages: English
• ISSNs: 0233-1888

Abstract

Abstract : We describe a procedure to introduce general dependence structures on a set of Dirichlet processes. Dependence can be in one direction to define a time series or in two directions to define spatial dependencies. More directions can also be considered. Dependence is induced via a set of latent processes and exploit the conjugacy property between the Dirichlet and the multinomial processes to ensure that the marginal law for each element of the set is a Dirichlet process. Dependence is characterized through the correlation between any two elements. Posterior distributions are obtained when we use the set of Dirichlet processes as prior distributions in a Bayesian nonparametric context. Posterior predictive distributions induce partially exchangeable sequences defined by generalized Pólya urns. A numerical example to illustrate is also included.