Characterizing variation of nonparametric random probability measures using the Kullback–Leibler divergence

References

• Hjort N, Holmes C, Müller P, et al. Bayesian nonparametrics. Cambridge: Cambridge University Press; 2010.
   Google Scholar
• Ghosh J, Ramamoorthi R. Bayesian nonparametrics. Vol. 1. Springer-Verlag, New York: Springer; 2003.
   Google Scholar
• Müller P, Quintana F. Nonparametric Bayesian data analysis. Statist Sci. 2004;19:95–110. doi: 10.1214/088342304000000017
   Web of Science ®Google Scholar
• Ferguson T. A Bayesian analysis of some nonparametric problems. Ann Stat. 1973;1:209–230. doi: 10.1214/aos/1176342360
   Web of Science ®Google Scholar
• Lavine M. Some aspects of Pólya tree distributions for statistical modelling. Ann Stat. 1992;20:1222–1235. doi: 10.1214/aos/1176348767
   Web of Science ®Google Scholar
• Karabatsos G. Bayesian nonparametric model selection and model testing. J Math Psychol. 2006;50:123–148. doi: 10.1016/j.jmp.2005.07.003
   Web of Science ®Google Scholar
• Muliere P, Walker S. A Bayesian non-parametric approach to survival analysis using Pólya trees. Scand J Stat. 1997;24:331–340. doi: 10.1111/1467-9469.00067
   Web of Science ®Google Scholar
• Walker SG, Damien P, Laud PW, Smith A. Bayesian nonparametric inference for random distributions and related functions. J R Statist Soc B (Statist Methodol). 1999;61:485–527. doi: 10.1111/1467-9868.00190
   Web of Science ®Google Scholar
• Hanson T, Johnson W. Modeling regression error with a mixture of Pólya trees. J Am Statist Assoc. 2002;97:1020–1033. doi: 10.1198/016214502388618843
   Web of Science ®Google Scholar
• Walker S, Mallick B. Hierarchical generalized linear models and frailty models with Bayesian nonparametric mixing. J R Statist Soc: B (Statist Methodol). 1997;59:845–860. doi: 10.1111/1467-9868.00101
   Web of Science ®Google Scholar
• Kullback S, Leibler R. On information and sufficiency. Ann Math Stat. 1951;22:79–86. doi: 10.1214/aoms/1177729694
   Google Scholar
• Kullback S. Information theory and statistics. New York: Wiley; 1959.
   Google Scholar
• Bernardo J, Smith A. Bayesian theory. New York: John Wiley & Sons; 1994.
   Google Scholar
• Cover T, Thomas J. Elements of information theory. New York: Wiley; 1991.
   Google Scholar
• Watson J, Holmes C. Approximate models and robust decisions. Statist Sci. 2016; to appear.
   PubMed Web of Science ®Google Scholar
• Ferguson T. Prior distributions on spaces of probability measures. Ann Stat. 1974;2:615–629. doi: 10.1214/aos/1176342752
   Web of Science ®Google Scholar
• Nieto-Barajas LE, Müller P. Rubbery Pólya tree. Scand J Stat. 2012;39:166–184. doi: 10.1111/j.1467-9469.2011.00761.x
   Web of Science ®Google Scholar
• Kraft C. A class of distribution function processes which have derivatives. J Appl Probab. 1964;1:385–388. doi: 10.1017/S0021900200108472
   Google Scholar
• McCulloch RE. Local model influence. J Am Statist Assoc. 1989;84:473–478. doi: 10.1080/01621459.1989.10478793
   Web of Science ®Google Scholar
• Efron B. Bootstrap methods: another look at the jackknife. Ann Stat. 1979;7:1–26. doi: 10.1214/aos/1176344552
   Web of Science ®Google Scholar
• Hansen LP, Sargent TJ. Robust control and model uncertainty. Am Econ Rev. 2001;91:60–66. doi: 10.1257/aer.91.2.60
   Web of Science ®Google Scholar
• Breuer T, Csiszár I. Measuring distribution model risk. Math Finance. 2016;26:395–411. doi: 10.1111/mafi.12050
   Web of Science ®Google Scholar
• Simpson DP, Martins TG, Riebler A, Fuglstad GA, Rue H, Sørbye SH. Penalising model component complexity: a principled, practical approach to constructing priors, arXiv preprint arXiv:1403.4630; 2014.
   Google Scholar
• Rubin D. The Bayesian bootstrap. Ann Stat. 1981;9:130–134. doi: 10.1214/aos/1176345338
   Web of Science ®Google Scholar
• Ishwaran H, Zarepour M. Dirichlet prior sieves in finite normal mixtures. Statist Sinica. 2002;12:941–963.
   Web of Science ®Google Scholar
• Hanson T. Inference for mixtures of finite Pólya tree models. J Am Statist Assoc. 2006;101:1548–1565. doi: 10.1198/016214506000000384
   Web of Science ®Google Scholar
• Gelman A, Carlin J, Stern H, Dunson D, Vehtari A, Rubin D. Bayesian data analysis. Boca Raton, FL: Chapman & Hall/CRC; 2013.
   Google Scholar
• Lo AY. On a class of Bayesian nonparametric estimates: I. Density estimates. Ann Stat. 1984;12:351–357. doi: 10.1214/aos/1176346412
   Web of Science ®Google Scholar