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On the stick–breaking representation of normalized inverse Gaussian priors

Author

Listed:
  • Stefano Favaro

    (University of Turin and Collegio Carlo Alberto)

  • Antonio Lijoi

    (Department of Economics and Management, University of Pavia and Collegio Carlo Alberto)

  • Igor Prünster

    (University of Turin and Collegio Carlo Alberto)

Abstract

Random probability measures are the main tool for Bayesian nonparametric inference, with their laws acting as prior distributions. Many well–known priors used in practice admit different, though (in distribution) equivalent, representations. Some of these are convenient if one wishes to thoroughly analyze the theoretical properties of the priors being used, others are more useful for modeling dependence and for addressing computational issues. As for the latter purpose, so–called stick–breaking constructions certainly stand out. In this paper we focus on the recently introduced normalized inverse Gaussian process and provide a completely explicit stick–breaking representation for it. Such a new result is of interest both from a theoretical viewpoint and for statistical practice.

Suggested Citation

  • Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    • Handle: RePEc:pav:demwpp:demwp0008
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    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0008.pdf
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    References listed on IDEAS

    as
    1. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
    2. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2007. "Bayesian Nonparametric Estimation of the Probability of Discovering New Species," Biometrika, Biometrika Trust, vol. 94(4), pages 769-786.
    3. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
    4. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2009. "Posterior Analysis for Normalized Random Measures with Independent Increments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 76-97, March.
    5. Lijoi, Antonio & Mena, Ramses H. & Prunster, Igor, 2005. "Hierarchical Mixture Modeling With Normalized Inverse-Gaussian Priors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1278-1291, December.
    6. Sonia Petrone & Michele Guindani & Alan E. Gelfand, 2009. "Hybrid Dirichlet mixture models for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 755-782, September.
    7. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2006. "Conjugacy as a Distinctive Feature of the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 105-120, March.
    8. Jason A. Duan & Michele Guindani & Alan E. Gelfand, 2007. "Generalized Spatial Dirichlet Process Models," Biometrika, Biometrika Trust, vol. 94(4), pages 809-825.
    9. C. Yau & O. Papaspiliopoulos & G. O. Roberts & C. Holmes, 2011. "Bayesian non‐parametric hidden Markov models with applications in genomics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 37-57, January.
    10. Dunson, David B. & Xue, Ya & Carin, Lawrence, 2008. "The Matrix Stick-Breaking Process: Flexible Bayes Meta-Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 317-327, March.
    11. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
    12. Ishwaran H. & James L. F, 2001. "Gibbs Sampling Methods for Stick Breaking Priors," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 161-173, March.
    13. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
    14. David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323.
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