Griffin, J. E.; Steel, M. F. J. Order-based dependent Dirichlet processes. (English) Zbl 1118.62360 J. Am. Stat. Assoc. 101, No. 473, 179-194 (2006). Summary: We propose a new framework for Bayesian nonparametric modeling with continuous covariates. In particular, we allow the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick-breaking representation. We focus mostly on the class of random distributions that induces a Dirichlet process at each covariate value. We derive the correlation between distributions at different covariate values and use a point process to implement a practically useful type of ordering. Two main constructions with analytically known correlation structures are proposed. Practical and efficient computational methods are introduced. We apply our framework, through mixtures of these processes, to regression modeling, the modeling of stochastic volatility in time series data, and spatial geostatistical modeling. Cited in 109 Documents MSC: 62M99 Inference from stochastic processes 62G99 Nonparametric inference 62F15 Bayesian inference PDFBibTeX XMLCite \textit{J. E. Griffin} and \textit{M. F. J. Steel}, J. Am. Stat. Assoc. 101, No. 473, 179--194 (2006; Zbl 1118.62360) Full Text: DOI