2016/03/31 by Georgios Papageorgiou · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian multivariate linear regression #Bayesian probability #Context (archaeology) #Covariate #Density estimation #Markov chain Monte Carlo #Multivariate statistics #Nonparametric regression #Quantile #Quantile regression #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #msc:6207 #msc:62G07 #stat.ME
paper · pdf · doi:10.1111/anzs.12273
published in Australian & New Zealand Journal of Statistics 61(3), 336-359 (Wiley) · 25 pages, 4 figures
openalex created_date 2016/06/24 · arxiv created 2019/08/13 · arxiv updated 2019/08/14 · openalex publication_date 2019/09/01 · openalex updated_date 2026/08/05
Summary We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densities from the multivariate ones. The approach to multivariate mixed scale outcome density estimation that we describe represents discrete variables, either responses or covariates, as discretised versions of continuous latent variables. We present and compare several models for obtaining these thresholds in the challenging context of count data analysis where the response may be over‐ and/or under‐dispersed in some of the regions of the covariate space. We utilise a nonparametric mixture of multivariate Gaussians to model the directly observed and the latent continuous variables. The paper presents a Markov chain Monte Carlo algorithm for posterior sampling, sufficient conditions for weak consistency, and illustrations on density, mean and quantile regression utilising simulated and real datasets.