Bayesian density regression with applications

In social science and biomedical applications, hierarchical models involving latent variables or random effects are very widely used. In studying relationships between latent and observed variables, it is standard practice to assume linearity and normality. Motivated by the need to develop flexible models that relax these assumptions, we propose new classes of priors for uncountable collections of dependent probability measures. For example, such priors can allow the density of a (latent or observed) response to change nonparametrically with multiple predictors. Focusing on a class of kernel stick-breaking processes, theoretical properties are briefly discussed, efficient computational methods are developed, and the approach is applied to various examples.