Weakly Informative Reparameterizations for Location-Scale Mixtures |
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Authors: | Kaniav Kamary Jeong Eun Lee Christian P Robert |
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Institution: | 1. CEREMADE, Université Paris-Dauphine, PSL Research University, Paris, France;2. INRIA, Saclay, Paris, France;3. Auckland University of Technology, Auckland, New Zealand;4. Department of Statistics, University of Warwick, Coventry, United Kingdom |
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Abstract: | While mixtures of Gaussian distributions have been studied for more than a century, the construction of a reference Bayesian analysis of those models remains unsolved, with a general prohibition of improper priors due to the ill-posed nature of such statistical objects. This difficulty is usually bypassed by an empirical Bayes resolution. By creating a new parameterization centered 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 Markov chain Monte Carlo (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 article. Supplementary material for this article is available online. |
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Keywords: | Bayesian analysis Compound distributions Dirichlet prior Exchangeability Improper prior Noninformative prior |
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