Skip to main content
SpringerLink
Log in

A note on convergence rates for posterior distributions via large deviations techniques

  • Note
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

This paper provides rates of convergence for a class of posterior distributions which are exchangeable with respect to a tree of partitions. The derivations rely on large deviations techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barron A, Schervish MJ, Wasserman L (1999) The consistency of distributions in nonparametric problems. Ann Stat 27: 536–561

    Article  MATH  MathSciNet  Google Scholar 

  • Dembo A, Zeitouni O (1998) Large deviations techniques and applications. Springer, New York

    MATH  Google Scholar 

  • Eichelsbacher P, Ganesh AJ (2002) Moderate deviations for Bayes posteriors. Scand J Stat 29: 153–167

    Article  MATH  MathSciNet  Google Scholar 

  • Ganesh AJ, O’Connell N (1999) An inverse of Sanov’s theorem. Stat Probab Lett 42: 201–206

    Article  MATH  MathSciNet  Google Scholar 

  • Ganesh AJ, O’Connell N (2000) A large deviation principle for Dirichlet posteriors. Bernoulli 6: 1021–1034

    Article  MATH  MathSciNet  Google Scholar 

  • Ghosal S (2001) Convergence rates for density estimation with Bernstein polynomials. Ann Stat 29: 1264–1280

    Article  MATH  MathSciNet  Google Scholar 

  • Ghosal S, Ghosh JK, Ramamoorthi RV (1999) Posterior consistency of Dirichlet mixtures in density estimation. Ann Stat 27: 143–158

    Article  MATH  MathSciNet  Google Scholar 

  • Ghosal S, Ghosh JK, van der Vaart AW (2000) Convergence rates of posterior distributions. Ann Stat 28: 500–531

    Article  MATH  Google Scholar 

  • Ghosal S, van der Vaart AW (2001) Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities. Ann Stat 29: 1233–1263

    Article  MATH  Google Scholar 

  • Ghosh JK, Ramamoorthi RV (2003) Bayesian nonparametrics. Springer, New York

    MATH  Google Scholar 

  • Royden HL (1988) Real analysis. Macmillan, New York

    MATH  Google Scholar 

  • Shen X, Wasserman L (2001) Rates of convergence of posterior distributions. Ann Stat 29: 687–714

    Article  MATH  MathSciNet  Google Scholar 

  • Walker SG (2004) New approaches to Bayesian consistency. Ann Stat 32: 2028–2043

    Article  MATH  Google Scholar 

  • Walker SG, Damien P, Lenk P (2004) On priors with a Kullback–Leibler property. J Am Stat Assoc 99: 404–408

    Article  MATH  MathSciNet  Google Scholar 

  • Walker SG, Lijoi A, Prünster I (2007) On rates of convergence for posterior distributions in infinite-dimensional models. Ann Stat 35: 738–746

    Article  MATH  Google Scholar 

  • Wasserman L (1998) Asymptotic properties of nonparametric Bayesian procedures. In: Practical nonparametric and semiparametric Bayesian statistics. Lecture notes in statist, vol 133. Springer, New York, pp 293–304

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica e Matematica, Università dell’Insubria, Via Valleggio 11, 22100, Como, Italy

    Andrea Martinelli

  2. Dipartimento di Economia Politica e Metodi Quantitativi, Università degli Studi di Pavia, Via San Felice 5, 27100, Pavia, Italy

    Matteo Ruggiero

  3. Institute of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NZ, UK

    Stephen G. Walker

Authors
  1. Andrea Martinelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matteo Ruggiero
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stephen G. Walker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matteo Ruggiero.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martinelli, A., Ruggiero, M. & Walker, S.G. A note on convergence rates for posterior distributions via large deviations techniques. Stat Papers 51, 337–347 (2010). https://doi.org/10.1007/s00362-008-0180-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-008-0180-x

Keywords

Mathematics Subject Classification (2000)

Search

Navigation