2016/01/06 by Kamary, Kaniav, Lee, Jeong Eun, Christian P. Robert +2
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Methodology (stat.ME) #Statistical Mechanics and Entropy #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1601.01178
openalex publication_date 2016/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
While mixtures of Gaussian distributions have been studied for more than a century (Pearson, 1894), the construction of a reference Bayesian analysis of those models still remains unsolved, with a general prohibition of the usage of improper priors (Fruwirth-Schnatter, 2006) due to the ill-posed nature of such statistical objects. This difficulty is usually bypassed by an empirical Bayes resolution (Richardson and Green, 1997). By creating a new parameterisation cantered on the mean and possibly the variance of the mixture distribution itself, we manage to develop here a weakly informative prior for a wide class of mixtures with an arbitrary number of components. We demonstrate that some posterior distributions associated with this prior and a minimal sample size are proper. We provide MCMC implementations that exhibit the expected exchangeability. We only study here the univariate case, the extension to multivariate location-scale mixtures being currently under study. An R package called Ultimixt is associated with this paper.