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Bayesian non-parametric inference for species variety with a two-parameter Poisson-Dirichlet process prior


  • Stefano Favaro
  • Antonio Lijoi
  • Ramsés H. Mena
  • Igor Prünster


A Bayesian non-parametric methodology has been recently proposed to deal with the issue of prediction within species sampling problems. Such problems concern the evaluation, conditional on a sample of size "n", of the species variety featured by an additional sample of size "m". Genomic applications pose the additional challenge of having to deal with large values of both "n" and "m". In such a case the computation of the Bayesian non-parametric estimators is cumbersome and prevents their implementation. We focus on the two-parameter Poisson-Dirichlet model and provide completely explicit expressions for the corresponding estimators, which can be easily evaluated for any sizes of "n" and "m". We also study the asymptotic behaviour of the number of new species conditionally on the observed sample: such an asymptotic result, combined with a suitable simulation scheme, allows us to derive asymptotic highest posterior density intervals for the estimates of interest. Finally, we illustrate the implementation of the proposed methodology by the analysis of five expressed sequence tags data sets. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssb:v:71:y:2009:i:5:p:993-1008

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    References listed on IDEAS

    1. 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.
    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. 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.
    4. Wang, Ji-Ping Z. & Lindsay, Bruce G., 2005. "A Penalized Nonparametric Maximum Likelihood Approach to Species Richness Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 942-959, September.
    5. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2007. "A Bayesian Nonparametric Method for Prediction in EST Analysis," ICER Working Papers - Applied Mathematics Series 16-2007, ICER - International Centre for Economic Research.
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    Cited by:

    1. 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.
    2. 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.
    3. repec:bla:scjsta:v:44:y:2017:i:1:p:230-248 is not listed on IDEAS

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