Abstract

Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, changeas a (parametric or nonparametric) function of predictors. However, it is notalways appropriate to assume a location/scale representation, where the errordistribution has unchanging shape over the predictor space. In fact, it oftenhappens in applied research that the distribution of responses under studychanges with predictors in ways that cannot be reasonably represented by afinite dimensional functional form. This can seriously affect the answers tothe scientific questions of interest, and therefore more general approaches areindeed needed. This gives rise to the study of fully nonparametric regressionmodels. We review some of the main Bayesian approaches that have beenemployed to define probability models where the complete response distributionmay vary flexibly with predictors.We focus on developments based onmodifications of the Dirichlet process, historically termed dependent Dirichletprocesses, and some of the extensions that have been proposed to tacklethis general problem using nonparametric approaches