Statistics and Its Interface

Volume 8 (2015)

Number 2

Special Issue on Modern Bayesian Statistics (Part II)

Guest Editor: Ming-Hui Chen (University of Connecticut)

Bayesian multivariate mixed-scale density estimation

Pages: 195 – 201



Antonio Canale (Department of Economics and Statistics, University of Turin, Italy; and Collegio Carlo Alberto, Moncalieri, Italy)

David B. Dunson (Department of Statistical Science, Duke University, Durham, North Carolina, U.S.A.)


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.


large support, mixed discrete and continuous, nonparametric Bayes, rate of posterior contraction, strong posterior consistency

Published 6 March 2015