Bayesian Nonparametric Models for Conditional Densities Based on Orthogonal Polynomials

The paper considers a nonparametric Bayesian model for conditional densities. The model considered is a mixture of orthogonal polynomials with a prior on the number of components. The use of orthogonal polynomials allows for a great deal of flexibility in applications while maintaining useful approximation properties. We provide the posterior contraction rate in the case of Legendre polynomials. The algorithm proposed allows for cross-dimensional moves, allowing it to choose the optimal number of terms in the series expansion conditional on a penalty parameter. We also provide Monte Carlo simulations that show how well the model approximates known distributions also in finite sample situations.