Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

Improving ABC for quantile distributions

  • Published:
Statistics and Computing Aims and scope Submit manuscript

Abstract

A new approximate Bayesian computation (ABC) algorithm is proposed specifically designed for models involving quantile distributions. The proposed algorithm compares favourably with two other ABC algorithms when applied to examples involving quantile distributions.

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

  • Allingham, D., King, R.A.R., Mengersen, K.L.: Bayesian estimation of quantile distributions. Stat. Comput. 19, 189–201 (2009)

    Article  MathSciNet  Google Scholar 

  • Beaumont, M.A., Zhang, W., Balding, D.J.: Approximate Bayesian computation in population genetics. Genetics 162, 2025–2035 (2002)

    Google Scholar 

  • Beaumont, M.A., Cornuet, J.-M., Marin, J.-M., Robert, C.P.: Adaptive approximate Bayesian computation. Biometrika 96, 983–990 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Blum, M.G.B., François, O.: Non-linear regression models for approximate Bayesian computation. Stat. Comput. 20, 63–73 (2010)

    Article  MathSciNet  Google Scholar 

  • Bortot, P., Coles, S., Sisson, S.: Inference for stereological extremes. J. Am. Stat. Assoc. 102, 84–92 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Drovandi, C.C., Pettitt, A.N.: Estimation of parameters for macroparasite population evolution using approximate Bayesian computation. Biometrics (2010). doi:10.1111/j.1541-0420.2010.01410.x

  • Früwirth-Schnatter, S.: Finite Mixture and Markov Switching Models. Springer, New York (2006)

    Google Scholar 

  • Freimer, M., Mudholkar, G., Kollia, G., Lin, C.: A study of the generalized Tukey-lambda family. Commun. Stat. Theory Methods 17, 3547–3567 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  • Gilchrist, W.: Regression revisited. Int. Stat. Rev. 76, 401–418 (2008)

    Article  Google Scholar 

  • Grelaud, A., Robert, C.P., Marin, J.-M., Rodolphe, F., Talay, J.-F.: ABC likelihood-free methods for model choice in Gibbs random fields. Bayesian Anal. 4, 427–442 (2009)

    Article  Google Scholar 

  • Hald, A.: Statistical Theory with Engineering Applications, Wiley, New York (1952), p. 568

    MATH  Google Scholar 

  • Haynes, M., Mengersen, K.: Bayesian estimation of g-and-k distributions using MCMC. Comput. Stat. 20, 7–30 (2005)

    Article  MathSciNet  Google Scholar 

  • Lin, T.I., Lee, J.C., Yen, S.Y.: Finite mixture modelling using the skew normal distribution. Stat. Sin. 17, 909–927 (2007)

    MathSciNet  MATH  Google Scholar 

  • Marjoram, P., Molitor, J., Plagnol, V., Tavaré, S.: Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. USA 100, 15324–15328 (2003)

    Article  Google Scholar 

  • Neal, R.M.: Slice sampling (with discussion). Ann. Stat. 31, 705–767 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Sisson, S.A., Fan, Y., Tanaka, M.M.: Sequential Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. USA 104, 1760–1765 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Sisson, S.A., Fan, Y., Tanaka, M.M.: Correction for Sisson et al. ‘Sequential Monte Carlo without likelihoods’. Proc. Natl. Acad. Sci. USA 106, 16889 (2009)

    Google Scholar 

  • Su, S.: Numerical maximum log likelihood estimation for generalized lambda distributions. Comput. Stat. Data Anal. 51, 3983–3998 (2007)

    Article  MATH  Google Scholar 

  • Tukey, J.W.: The practical relationship between common transformations of percentages or fractions and of amounts. In: Mallows, C.L. (ed.) The Collected Works of John W. Tukey, vol. VI, pp. 211–219. Wadsworth Advanced Books & Software, Belmont (1984)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia

    R. McVinish

Authors
  1. R. McVinish
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. McVinish.

Additional information

Research supported by the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

McVinish, R. Improving ABC for quantile distributions. Stat Comput 22, 1199–1207 (2012). https://doi.org/10.1007/s11222-010-9209-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11222-010-9209-9

Keywords

Search

Navigation