Premium
Separation measures and the geometry of Bayes factor selection for classification
Author(s) -
Smith Jim Q.,
Anderson Paul E.,
Liverani Silvia
Publication year - 2008
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2008.00664.x
Subject(s) - hyperparameter , conjugacy class , bayes factor , separation (statistics) , mathematics , bayes' theorem , selection (genetic algorithm) , model selection , partition (number theory) , measure (data warehouse) , bayesian probability , computer science , artificial intelligence , machine learning , statistics , algorithm , combinatorics , data mining
Summary. 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.