Posterior Impropriety of some Sparse Bayesian Learning Models
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Sparse Bayesian learning models are typically used for prediction in datasets with significantly greater number of covariates than observations. Among the class of sparse Bayesian learning models, relevance vector machines (RVM) is very popular. Its popularity is demonstrated by a large number of citations of the original RVM paper of Tipping (2001)[JMLR, 1, 211 - 244]. In this article we show that RVM and some other sparse Bayesian learning models with hyperparameter values currently used in the literature are based on improper posteriors. Further, we also provide necessary and sufficient conditions for posterior propriety of RVM.
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