Annals of Statistics

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

Subhashis Ghosal

Full-text: Open access

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aos/1434546210

Digital Object Identifier
doi:10.1214/15-AOS1270E

Mathematical Reviews number (MathSciNet)
MR3357866

Zentralblatt MATH identifier
1321.62041

Citation

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. https://projecteuclid.org/euclid.aos/1434546210


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References

  • 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.