Bayesian Density Estimation Under Probabilistic First Moment Constraints

• Activity Number: 26
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Alejandro Jara*+
• Companies: Pontificia Universidad Católica de Chile
• Keywords: Bayesian nonparametrics ; Mean constraints ; Random sequential barycenter arrays

Abstract

In many statistical problems it is needed to place constraints on the location of probability distributions for the sake of identiability. For instance, in regression and hierarchical models, such constraints are needed to give an interpretation to location parameter. Consequently, Bayesian nonparametric (BNP) generalizations of the problem must appropriately restrict the trajectories of the processes. Although quantile constraints can be incorporated in a simple way for most of the commonly used BNP models, imposing moments constraints in such models is much more challenging. Furthermore, the calculation of the induced distribution for these functionals is difficult, thus difficulting the prior elicitation process. This work introduces and illustrates a general method for constructing random probability measures with densities w.r.t. the Lebesgue measure and prescribed mean or distribution of the mean, thus facilitating the independent prior specification on the different aspects of the density estimation problem. The proposal is based on mixtures induced by random sequential barycenter array probability measures. ** Supported by FONDECYT 11100144 grant.