Sufficient conditions for Bayesian consistency

Summary, in English

We introduce the Hausdorff α-entropy to study the strong Hellinger consistency of posterior distributions. We obtain general Bayesian consistency theorems which extend the well-known results of Barron et al. [1999. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 536–561] and Ghosal et al. [1999. Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27, 143–158] and Walker [2004. New approaches to Bayesian consistency. Ann. Statist. 32, 2028–2043]. As an application we strengthen previous results on Bayesian consistency of the (normal) mixture models.

• Författare: Yang Xing; Bo Ranneby
• Publiceringsår: 2009
• Språk: Engelska
• Sidor: 2479-2489
• Publikation/Tidskrift/Serie: Journal of Statistical Planning and Inference
• Volym: 139
• Issue: 7
• Länkar: http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V0M-4V1TXRG-2-1&_cdi=5650&_user=745831&_orig=search&_coverDate=07%2F01%2F2009&_sk=998609992&view=c&wchp=dGLzVtz-zSkWA&_valck=1&md5=26ae78f4b2906952bdac231182963eba&ie=/sdarticle.pdf; http://dx.doi.org/10.1016/j.jspi.2008.11.008
• Dokumenttyp: Artikel i tidskrift
• Förlag: North-Holland
• Ämne: Mathematics
• Nyckelord: Infinite-dimensional model; Sieve; Posterior distribution; Hellinger consistency
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 1873-1171