ArticleJournal of multivariate analysis2013
Posterior consistency in conditional distribution estimation.
Article in Journal of multivariate analysis, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- A Tree Perspective on Stick-Breaking Models in Covariate-Dependent Mixtures (with Discussion).Bayesian analysis · 2025Article
- Flexible Bayesian Product Mixture Models for Vector Autoregressions.Journal of machine learning research : JMLR · 2024Article
- Obesity and labour market outcomes in Italy: a dynamic panel data evidence with correlated random effects.The European journal of health economics : HEPAC : health economics in prevention and care · 2023Article
- A Conditional Density Estimation Partition Model Using Logistic Gaussian Processes.Biometrika · 2020Article
- Bayesian partial linear model for skewed longitudinal data.Biostatistics (Oxford, England) · 2015Article
- Bayesian factorizations of big sparse tensors.Journal of the American Statistical Association · 2015Article
- A Predictive Study of Dirichlet Process Mixture Models for Curve Fitting.Scandinavian journal of statistics, theory and applications · 2014Article
- Bayesian nonparametric regression with varying residual density.Annals of the Institute of Statistical Mathematics · 2014Article
- Simplex Factor Models for Multivariate Unordered Categorical Data.Journal of the American Statistical Association · 2012Article
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Authors and funding
3 authors.
Funding
Abstract
A wide variety of priors have been proposed for nonparametric Bayesian estimation of conditional distributions, and there is a clear need for theorems providing conditions on the prior for large support, as well as posterior consistency. Estimation of an uncountable collection of conditional distributions across different regions of the predictor space is a challenging problem, which differs in some important ways from density and mean regression estimation problems. Defining various topologies on the space of conditional distributions, we provide sufficient conditions for posterior consistency focusing on a broad class of priors formulated as predictor-dependent mixtures of Gaussian kernels. This theory is illustrated by showing that the conditions are satisfied for a class of generalized stick-breaking process mixtures in which the stick-breaking lengths are monotone, differentiable functions of a continuous stochastic process. We also provide a set of sufficient conditions for the case where stick-breaking lengths are predictor independent, such as those arising from a fixed Dirichlet process prior.
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