Bayesian multivariate mixed-scale density estimation

Journal Article (Journal Article)

Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to jointly model continuous, count and categorical variables under a nonparametric prior, which is induced through rounding latent variables having an unknown density with respect to Lebesgue measure. For the proposed class of priors, we provide sufficient conditions for large support, strong consistency and rates of posterior contraction. These conditions allow one to convert sufficient conditions obtained in the setting of multivariate continuous density estimation to the mixed scale case. To illustrate the procedure, a rounded multivariate nonparametric mixture of Gaussians is introduced and applied to a crime and communities dataset.

Full Text

Duke Authors

Cited Authors

  • Canale, A; Dunson, DB

Published Date

  • January 1, 2015

Published In

Volume / Issue

  • 8 / 2

Start / End Page

  • 195 - 201

Electronic International Standard Serial Number (EISSN)

  • 1938-7997

International Standard Serial Number (ISSN)

  • 1938-7989

Digital Object Identifier (DOI)

  • 10.4310/SII.2015.v8.n2.a7

Citation Source

  • Scopus