The Library
On choosing mixture components via non-local priors
Tools
Fuquene, Jairo, Steel, Mark F. J. and Rossell, David (2019) On choosing mixture components via non-local priors. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 81 (5). pp. 809-837. doi:10.1111/rssb.12333 ISSN 1369-7412.
|
PDF
WRAP-on-choosing-mixture-components-via-non-local-Steel-2019.pdf - Accepted Version - Requires a PDF viewer. Download (1625Kb) | Preview |
Official URL: https://doi.org/10.1111/rssb.12333
Abstract
Choosing the number of mixture components remains an elusive challenge. Model selection criteria can be either overly liberal or conservative and return poorly separated components of limited practical use. We formalize non‐local priors (NLPs) for mixtures and show how they lead to well‐separated components with non‐negligible weight, interpretable as distinct subpopulations. We also propose an estimator for posterior model probabilities under local priors and NLPs, showing that Bayes factors are ratios of posterior‐to‐prior empty cluster probabilities. The estimator is widely applicable and helps to set thresholds to drop unoccupied components in overfitted mixtures. We suggest default prior parameters based on multimodality for normal–T‐mixtures and minimal informativeness for categorical outcomes. We characterize theoretically the NLP‐induced sparsity, derive tractable expressions and algorithms. We fully develop normal, binomial and product binomial mixtures but the theory, computation and principles hold more generally. We observed a serious lack of sensitivity of the Bayesian information criterion, insufficient parsimony of the Akaike information criterion and a local prior, and a mixed behaviour of the singular Bayesian information criterion. We also considered overfitted mixtures; their performance was competitive but depended on tuning parameters. Under our default prior elicitation NLPs offered a good compromise between sparsity and power to detect meaningfully separated components.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | Journal of the Royal Statistical Society: Series B (Statistical Methodology) | ||||||||
Publisher: | Wiley-Blackwell Publishing Ltd. | ||||||||
ISSN: | 1369-7412 | ||||||||
Official Date: | November 2019 | ||||||||
Dates: |
|
||||||||
Volume: | 81 | ||||||||
Number: | 5 | ||||||||
Page Range: | pp. 809-837 | ||||||||
DOI: | 10.1111/rssb.12333 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | "This is the peer reviewed version of the following article: Fúquene, J. , Steel, M. and Rossell, D. (2019), On choosing mixture components via non‐local priors. J. R. Stat. Soc. B., which has been published in final form at https://doi.org/10.1111/rssb.12333. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions." | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 20 June 2019 | ||||||||
Date of first compliant Open Access: | 5 August 2020 | ||||||||
Related URLs: | |||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year