A colleague sent along the March 2011 issue of the ISBA Bulletin in which Michael Jordan lists the top five open problems in Bayesian statistics. The doyen at the intersection of ML/statistics/Bayesian stuff polled his peers and came up with this list:
- Model selection and hypothesis selection: Given data, how do we select from a set of potential models? How can we be certain that our selection was correct?
- Computation and statistics: When MCMC is too slow/infeasible, what do we do? More importantly: “Several respondents asked for a more thorough integration of computational science and statistical science, noting that the set of inferences that one can reach in any given situation are jointly a function of the model, the prior, the data and the computational resources, and wishing for more explicit management of the tradeoffs among these quantities.”
- Bayesian/frequentist relationships: This is getting at the situation for high dimensional models when a subjective prior is hard to specify, and a simple prior is misleading. Can we then “…give up some Bayesian coherence in return for some of the advantages of the frequentist paradigm, including simplicity of implementation and computational tractability”?
- Priors: No surprise here. One resondent had a fascinating comment: when we want to model data that arises from human behavior and human beliefs, then we would expect/desire effects on both the prior and likelihood. Then what do we do?
- Nonparametrics and semi-parametrics: What are the classes of problems for which NP Bayes methods are appropriate/”worth the trouble”? In NLP, clustering (i.e., using DP priors) is certainly an area in which nonparametrics have been successful.
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