Bayesian Nonparametric Inference for the Power Likelihood

References

• Barron , A. , Schervish , M. J. and Wasserman , L. 1999 . “The Consistency of Posterior Distributions in Nonparametric Problems,” . The Annals of Statistics , 27 : 536 – 561 .
   Web of Science ®Google Scholar
• Besag , J. and Green , P. J. 1993 . “Spatial Statistics and Bayesian Computation,” . Journal of the Royal Statistical Society, Series B , 55 : 25 – 37 .
   Google Scholar
• Damien , P. , Wakefield , J. and Walker , S. 1999 . “Gibbs Sampling for Bayesian Non-Conjugate and Hierarchical Models by Using Auxiliary Variables,” . Journal of the Royal Statistical Society, Series B , 61 : 331 – 344 .
   Google Scholar
• Escobar , M. D. 1988 . “Estimating the Means of Several Normal Populations by Nonparametric Estimation of the Distribution of the Means,” . Ph.D. dissertation, Department of Statistics, Yale University
   Google Scholar
• Ferguson , T. S. 1973 . “A Bayesian Analysis of Some Nonparametric Problems,” . The Annals of Statistics , 1 : 209 – 230 .
   Web of Science ®Google Scholar
• Friel , N. and Pettitt , A. N. 2008 . “Marginal Likelihood Estimation via Power Posteriors,” . Journal of the Royal Statistical Society, Series B , 70 : 589 – 607 .
   Google Scholar
• Ghosal , S. , Ghosh , J. K. and Ramamoorthi , R. V. 1999 . “Posterior Consistency of Dirichlet Mixtures in Density Estimation,” . The Annals of Statistics , 27 : 143 – 158 .
   Web of Science ®Google Scholar
• Godsill , S. J. 2001 . “On the Relationship Between Markov Chain Monte Carlo Methods for Model Uncertainty,” . Journal of Computational and Graphical Statistics , 10 : 230 – 248 .
   Web of Science ®Google Scholar
• Green , P. J. 1995 . “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination,” . Biometrika , 82 : 711 – 732 .
   Web of Science ®Google Scholar
• Hjort , N. L. , Holmes , C. , Müller , P. and Walker , S. G. 2010 . Bayesian Nonparametrics , New York : Cambridge University Press .
   Google Scholar
• Ibrahim , J. G. and Chen , M. H. 2000 . “Power Prior Distributions for Regression Models,” . Statistical Science , 15 : 46 – 60 .
   Web of Science ®Google Scholar
• Ishwaran , H. and James , L. F. 2001 . “Gibbs Sampling Methods for Stick Breaking Priors,” . Journal of the American Statistical Association , 96 : 161 – 173 .
   Web of Science ®Google Scholar
• Kalli , M. , Griffin , J. E. and Walker , S. G. 2011 . “Slice Sampling Mixture Models,” . Statistics and Computing , 21 : 93 – 105 .
   Web of Science ®Google Scholar
• Lo , A. Y. 1984 . “On a Class of Bayesian Nonparametric Estimates: I. Density Estimates,” . The Annals of Statistics , 12 : 351 – 357 .
   Web of Science ®Google Scholar
• MacEachern , S. N. and Müller , P. 1998 . “Estimating Mixture of Dirichlet Process Models,” . Journal of Computational and Graphical Statistics , 7 : 223 – 238 .
   Web of Science ®Google Scholar
• Neal , R. M. 2000 . “Markov Chain Sampling Methods for Dirichlet Process Mixture Models,” . Journal of Computational and Graphical Statistics , 9 : 249 – 265 .
   Web of Science ®Google Scholar
• Papaspiliopoulos , O. and Roberts , G. O. 2008 . “Retrospective Markov Chain Monte Carlo Methods for Dirichlet Process Hierarchical Models,” . Biometrika , 95 : 169 – 186 .
   Web of Science ®Google Scholar
• Sethuraman , J. 1994 . “A Constructive Definition of Dirichlet Priors,” . Statistica Sinica , 4 : 639 – 650 .
   Web of Science ®Google Scholar
• Walker , S. G. 2004 . “New Approaches to Bayesian Consistency,” . The Annals of Statistics , 32 : 2028 – 2043 .
   Web of Science ®Google Scholar
• Walker , S. G. and Hjort , N. L. 2001 . “On Bayesian Consistency,” . Journal of the Royal Statistical Society, Series B , 63 : 811 – 821 .
   Google Scholar