Learning Bounds for a Generalized Family of Bayesian Posterior Distributions

Part of Advances in Neural Information Processing Systems 16 (NIPS 2003)

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Tong Zhang


In this paper we obtain convergence bounds for the concentration of Bayesian posterior distributions (around the true distribution) using a novel method that simplifies and enhances previous results. Based on the analysis, we also introduce a generalized family of Bayesian posteriors, and show that the convergence behavior of these generalized posteriors is completely determined by the local prior structure around the true distri- bution. This important and surprising robustness property does not hold for the standard Bayesian posterior in that it may not concentrate when there exist “bad” prior structures even at places far away from the true distribution.