Posterior impropriety of some sparse Bayesian learning models

Anand Dixit and Vivekananda Roy

Statistics & Probability Letters, 2021, vol. 171, issue C

Abstract: 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.

Keywords: Improper prior; Jeffreys’ prior; Posterior propriety; Relevance vector machine; Reproducing kernel Hilbert spaces; Sparsity (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109039

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