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Separation measures and the geometry of Bayes factor selection for classification
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Smith, J. Q., Anderson, Paul E. and Liverani, Silvia (2008) Separation measures and the geometry of Bayes factor selection for classification. Journal of the Royal Statistical Society Series B: Statistical Methodology, Vol.70 (No.5). pp. 957-980. doi:10.1111/j.1467-9868.2008.00664.x ISSN 1369-7412.
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Official URL: http://dx.doi.org/10.1111/j.1467-9868.2008.00664.x
Abstract
Conjugacy assumptions are often used in Bayesian selection over a partition because they allow the otherwise unfeasibly large model space to be searched very quickly. The implications of such models can be analysed algebraically. We use the explicit forms of the associated Bayes factors to demonstrate that such methods can be unstable under common settings of the associated hyperparameters. We then prove that the regions of instability can be removed by setting the hyperparameters in an unconventional way. Under this family of assignments we prove that model selection is determined by an implicit separation measure: a function of the hyperparameters and the sufficient statistics of clusters in a given partition. We show that this family of separation measures has plausible properties. The methodology proposed is illustrated through the selection of clusters of longitudinal gene expression profiles.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics Faculty of Science, Engineering and Medicine > Research Centres > Warwick Systems Biology Centre |
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Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Cluster analysis | ||||
Journal or Publication Title: | Journal of the Royal Statistical Society Series B: Statistical Methodology | ||||
Publisher: | Wiley-Blackwell Publishing, Inc | ||||
ISSN: | 1369-7412 | ||||
Official Date: | November 2008 | ||||
Dates: |
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Volume: | Vol.70 | ||||
Number: | No.5 | ||||
Number of Pages: | 24 | ||||
Page Range: | pp. 957-980 | ||||
DOI: | 10.1111/j.1467-9868.2008.00664.x | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), University of Warwick. Centre for Research in Statistical Methodology |
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