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D.B. Dunson 289ing background, and in the applications they face, speed is everything andcharacterizing uncertainty in inference or testing is just not a problem theyencounter. In fact, ML researchers working on NP Bayes methods seldom reportinferences or use uncertainty in their analyses; they instead use NP Bayesmethods combined with approximations, such as variational Bayes or expectationpropagation, to improve performance on ML tasks, such as prediction.Often predictive performance can be improved, while avoiding cross-validationfor tuning parameter selection, and these gains have partly led to the relativepopularity of NP Bayes in machine learning.It is amazing to me how many fascinating and important unsolved problemsremain in NP Bayes, with the solutions having the potential to substantiallyimpact practice in analyzing and interpreting data in many fields.For example, there is no work on the above nonparametric Bayes graphicalmodeling problem, though we have developed an initial approach we willsubmit for publication soon. There is very limited work on fast and scalableapproximations to the posterior distribution in Bayesian nonparametric models.Markov chain Monte Carlo (MCMC) algorithms are still routinely useddespite their problems with scalability due to the lack of decent alternatives.Variational Bayes and expectation propagation algorithms developed in MLlack theoretical guarantees and often perform poorly, particularly when thefocus goes beyond obtaining a point estimate for prediction. Sequential MonteCarlo (SMC) algorithms face similar scalability problems to MCMC, with adaunting number of particles needed to obtain adequate approximations forhigh-dimensional models. There is a clear need for new models for flexibledimensionality reduction in broad settings. There is a clear lack of approachesfor complex non-Euclidean data structures, such as shapes, trees, networksand other object data.Ihopethatthischapterinspiresatleastafewyoungresearcherstofocuson improving the state of the art in NP Bayes statistics. The most effectivepath to success and high impact in my view is to focus on challengingreal-world applications in which current methods have obvious inadequacies.Define innovative probability models for these data, develop new scalable approximationsand computational algorithms, study the theoretical properties,implement the methods on real data, and provide software packages for routineuse. Given how few people are working in such areas, there are manylow hanging fruit and the clear possibility of major breakthroughs, which areharder to achieve when jumping on bandwagons.ReferencesBhattacharya, A., Pati, D., and Dunson, D.B. (2013). Anisotropic functionestimation using multi-bandwidth Gaussian processes. The Annals