Bayesian Nonparametrics by Nils Lid Hjort, Chris Holmes, Peter Müller, Stephen G.

By Nils Lid Hjort, Chris Holmes, Peter Müller, Stephen G. Walker

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2 Bayesian choices 25 undertake prior to posterior analysis. How large a prior should be is a clear matter. It is large enough so that no matter what subsequently occurs, the prior is not checked. Hence, in may cases, it is only going to be a nonparametric model that is going to suffice. If a Bayesian has a prior distribution and suspects there is additional uncertainty, there are two possible actions. The first is to consider an alternative prior and then select one or the other after the data have been observed.

2006). All of Nonparametric Statistics: A Concise Course in Nonparametric Statistical Inference. New York: Springer-Verlag. Wasserman, L. (2008). Comment on article by Gelman. Bayesian Analysis 3, ed. J. , 463–6. Oxford: Oxford University Press. 1 Bayesian nonparametric methods: motivation and ideas Stephen G. Walker It is now possible to demonstrate many applications of Bayesian nonparametric methods. It works. It is clear, however, that nonparametric methods are more complicated to understand, use and derive conclusions from, when compared to their parametric counterparts.

Green, N. L. Hjort, and S. Richardson, 455–87. Oxford: Oxford University Press. Hjort, N. L. and Walker, S. G. (2009). Quantile pyramids for Bayesian nonparametrics. Annals of Statistics, 37, 105–31. Holmes, C. C. and Mallick, B. (2000). Bayesian wavelet networks for nonparametric regression. IEEE Transactions on Neural Networks, 11, 27–35. Ibrahim, J. -H. and Sinha, D. (2001). Bayesian Survival Analysis. New York: Springer-Verlag. Jara, A. (2007). Applied Bayesian non- and semi-parametric inference using DPpackage.

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