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Bayesian nonparametric estimators derived from conditional Gibbs structures

Author

Listed:
  • Antonio Lijoi
  • Igor Pruenster
  • Stephen G. Walker

Abstract

We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian nonparametric estimators, which can be readily exploited for predicting various features of additional samples. The results provide useful tools for genomic applications where prediction of future outcomes is required.

Suggested Citation

  • Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Bayesian nonparametric estimators derived from conditional Gibbs structures," ICER Working Papers - Applied Mathematics Series 06-2008, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:06-2008
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    File URL: http://www.bemservizi.unito.it/repec/icr/wp2008/ICERwp06-08.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Chang Xuan Mao, 2004. "Predicting the Conditional Probability of Discovering a New Class," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1108-1118, December.
    3. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    4. Lancelot F. James & Antonio Lijoi & Igor Pruenster, 2005. "Bayesian Inference via Classes of Normalized Random Measures," ICER Working Papers - Applied Mathematics Series 5-2005, ICER - International Centre for Economic Research.
    5. 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.
    6. 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.
    7. Chang Xuan Mao, 2002. "A Poisson model for the coverage problem with a genomic application," Biometrika, Biometrika Trust, vol. 89(3), pages 669-682, August.
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    Citations

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    Cited by:

    1. Masaaki Sibuya, 2014. "Prediction in Ewens–Pitman sampling formula and random samples from number partitions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 833-864, October.
    2. Pierpaolo De Blasi & Stefano Favaro & Antonio Lijoi & Ramsés H. Mena & Igor Prünster & Mattteo Ruggiero, 2013. "Are Gibbs-type priors the most natural generalization of the Dirichlet process?," DEM Working Papers Series 054, University of Pavia, Department of Economics and Management.
    3. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "A new estimator of the discovery probability," DEM Working Papers Series 007, University of Pavia, Department of Economics and Management.
    4. Stefano Favaro & Antonio Lijoi & Igor Prunster, 2011. "Asymptotics for a Bayesian nonparametric estimator of species richness," Quaderni di Dipartimento 144, University of Pavia, Department of Economics and Quantitative Methods.
    5. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    6. Cesari, Oriana & Favaro, Stefano & Nipoti, Bernardo, 2014. "Posterior analysis of rare variants in Gibbs-type species sampling models," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 79-98.
    7. Stefano Favaro & Shui Feng & Fuqing Gao, 2018. "Moderate Deviations for Ewens-Pitman Sampling Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 330-341, August.
    8. Mena, Ramsés H. & Walker, Stephen G., 2012. "An EPPF from independent sequences of geometric random variables," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1059-1066.
    9. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "A New Estimator of the Discovery Probability," Biometrics, The International Biometric Society, vol. 68(4), pages 1188-1196, December.
    10. Antonio Lijoi & Igor Pruenster, 2009. "Models beyond the Dirichlet process," ICER Working Papers - Applied Mathematics Series 23-2009, ICER - International Centre for Economic Research.
    11. Shuhei Mano, 2017. "Extreme sizes in Gibbs-type exchangeable random partitions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 1-37, February.
    12. Stefano Favaro & Igor Prünster & Stephen G. Walker, 2012. "On a Generalized Chu–Vandermonde Identity," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 253-262, June.
    13. Stefano Favaro & Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2009. "Bayesian non‐parametric inference for species variety with a two‐parameter Poisson–Dirichlet process prior," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 993-1008, November.

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