  Sparse Bayesian learning models are typically used for prediction in datasets
with significantly greater number of covariates than observations. Such models
often take a reproducing kernel Hilbert space (RKHS) approach to carry out the
task of prediction and can be implemented using either proper or improper
priors. In this article we show that a few sparse Bayesian learning models in
the literature, when implemented using improper priors, lead to improper
posteriors.
