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Weakly informative reparameterisations for location-scale mixtures
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Kamary, Kaniav, Lee, Jeong Eun and Robert, Christian P. (2018) Weakly informative reparameterisations for location-scale mixtures. Journal of Computational and Graphical Statistics, 27 (4). pp. 836-848. doi:10.1080/10618600.2018.1438900 ISSN 1061-8600.
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Official URL: https://doi.org/10.1080/10618600.2018.1438900
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 (Frühwirth-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 centred 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.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
| Library of Congress Subject Headings (LCSH): | Gaussian distribution, Bayesian statistical decision theory, Coordinates, Polar, Mixture distributions (Probability theory) | ||||||
| Journal or Publication Title: | Journal of Computational and Graphical Statistics | ||||||
| Publisher: | American Statistical Association | ||||||
| ISSN: | 1061-8600 | ||||||
| Official Date: | 13 February 2018 | ||||||
| Dates: |
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| Volume: | 27 | ||||||
| Number: | 4 | ||||||
| Page Range: | pp. 836-848 | ||||||
| DOI: | 10.1080/10618600.2018.1438900 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 3 May 2018 | ||||||
| Date of first compliant Open Access: | 13 February 2019 | ||||||
| Open Access Version: |
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