Annals of Statistics

Discussion of “Frequentist coverage of adaptive nonparametric Bayesian credible sets”

Subhashis Ghosal

Full-text: Open access

Article information

Ann. Statist., Volume 43, Number 4 (2015), 1455-1462.

Received: January 2015
First available in Project Euclid: 17 June 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Ghosal, Subhashis. Discussion of “Frequentist coverage of adaptive nonparametric Bayesian credible sets”. Ann. Statist. 43 (2015), no. 4, 1455--1462. doi:10.1214/15-AOS1270E.

Export citation


  • Castillo, I. and Nickl, R. (2013). Nonparametric Bernstein–von Mises theorems in Gaussian white noise. Ann. Statist. 41 1999–2028.
  • Cox, D. D. (1993). An analysis of Bayesian inference for nonparametric regression. Ann. Statist. 21 903–923.
  • Freedman, D. (1999). On the Bernstein–von Mises theorem with infinite-dimensional parameters. Ann. Statist. 27 1119–1140.
  • Giné, E. and Nickl, R. (2011). Rates on contraction for posterior distributions in $L^{r}$-metrics, $1\leq r\leq\infty$. Ann. Statist. 39 2883–2911.
  • Knapik, B. T., van der Vaart, A. W. and van Zanten, J. H. (2011). Bayesian inverse problems with Gaussian priors. Ann. Statist. 39 2626–2657.
  • Leahu, H. (2011). On the Bernstein–von Mises phenomenon in the Gaussian white noise model. Electron. J. Stat. 5 373–404.
  • Ledoux, M. and Talagrand, M. (1991). Probability in Banach Spaces: Isoperimetry and Processes. Ergebnisse der Mathematik und Ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)] 23. Springer, Berlin.
  • Rivoirard, V. and Rousseau, J. (2012). Bernstein–von Mises theorem for linear functionals of the density. Ann. Statist. 40 1489–1523.
  • van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes: With Applications to Statistics. Springer Series in Statistics. Springer, New York.
  • Yoo, W. W. and Ghosal, S. (2014). Supremum norm posterior contraction and credible sets for nonparametric multivariate regression. Available at arXiv:1411.6716.

See also

  • Main article: Frequentist coverage of adaptive nonparametric Bayesian credible sets.