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Challenges in implementing the Bayesian paradigm

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If you have a question about this talk, please contact Zoubin Ghahramani.

The optimality properties of Bayesian inference are well established, and yet there remains a wide gulf between the mathematical foundations of the methods and practical implementation. The gap shows up most strongly in specification of the prior distribution, particularly when the analyst has (or wishes to inject) little information about the parameters. In such cases, the prior distribution often depends on the data itself, and this dependence is routinely ignored in the subsequent analysis. In this talk, we formalize the notion of a data dependent prior distribution and show how to bring the analysis into agreement with Bayes Theorem. Properties of the adjustment are described, and a range of impacts on posterior inference is illustrated. The impact is particularly large in high and infinite dimensional settings, such as those characterizing nonparametric Bayesian inference. In this high-dimensional setting, a quick description of the need for additional adjustments to traditional Bayesian concepts such as the Bayes factor will be given.

The work on data dependent prior distributions is joint with Bill Darnieder; that on Bayes factors is joint with Xinyi Xu, Pingbo Lu, and Ruoxi Xu.

This talk is part of the Machine Learning @ CUED series.

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