On the Frequentist Properties of Bayesian Nonparametric Methods
Rousseau, Judith (2016), On the Frequentist Properties of Bayesian Nonparametric Methods, Annual Reviews of Statistics and its applications, 3:211-231, p. 24. 10.1146/annurev-statistics-041715-033523
TypeArticle accepté pour publication ou publié
External document linkhttps://www.ceremade.dauphine.fr/~rousseau/statreviews.pdf
Journal nameAnnual Reviews of Statistics and its applications
MetadataShow full item record
Abstract (EN)In this paper, I review the main results on the asymptotic properties of the posterior distribution in nonparametric or high-dimensional models. In particular, I explain how posterior concentration rates can be derived and what we learn from such analysis in terms of the impact of the prior distribution on high-dimensional models. These results concern fully Bayes and empirical Bayes procedures. I also describe some of the results that have been obtained recently in semiparametric models, focusing mainly on the Bernstein–von Mises property. Although these results are theoretical in nature, they shed light on some subtle behaviors of the prior models and sharpen our understanding of the family of functionals that can be well estimated for a given prior model.
Subjects / Keywordsasymptotics; Bayesian nonparametrics; Bernstein–von Mises; posterior concentration; empirical Bayes
Showing items related by title and author.
On some aspects of the asymptotic properties of Bayesian approaches in nonparametric and semiparametric models Scricciolo, Catia; Salomond, Jean-Bernard; Rousseau, Judith (2014-01-30) Communication / Conférence
Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process Rousseau, Judith; Chopin, Nicolas; Liseo, Brunero (2012) Article accepté pour publication ou publié
Bayesian nonparametric dependent model for partially replicated data: The influence of fuel spills on species diversity Arbel, Julyan; Mengersen, Kerrie; Rousseau, Judith (2016) Article accepté pour publication ou publié