Open problems in Bayesian statistics

In a recent bulletin for the International Society for Bayesian Statistics, the new president, Michael Jordan, requested responses from top academic Bayesians and asked them what the currently open problems are in Bayesian statistics. As a quick summary, the list is (in Michael Jordan's order):

1. Model selection and hypothesis testing
2. Computation and statistics
3. Bayesian/frequentist relationships
4. Priors
5. Nonparametrics and semiparametrics

Some additional discussion by Andrew Gelman can be found at the statistics forum. I thought this list and the associated discussion would be useful for graduate students who are entertaining a thesis in Bayesian statistics.

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