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Sampling designs via a multivariate hypergeometric-Dirichlet process model for a multi-species assemblage with unknown heterogeneity

  • Zhang, Hongmei
  • Ghosh, Kaushik
  • Ghosh, Pulak
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    In a sample of mRNA species counts, sequences without duplicates or with small numbers of copies are likely to carry information related to mutations or diseases and can be of great interest. However, in some situations, sequence abundance is unknown and sequencing the whole sample to find the rare sequences is not practically possible. To collect mRNA sequences of interest, or more generally, species of interest, we propose a two-phase Bayesian sampling method that addresses these concerns. The first phase of the design is used to infer sequence (species) abundance levels through a cluster analysis applied to a pilot data set. The clustering method is built upon a multivariate hypergeometric model with a Dirichlet process prior for species relative frequencies. The second phase, through Monte Carlo simulations, infers the sample size necessary to collect a certain number of species of particular interest. Efficient posterior computing schemes are proposed. The developed approach is demonstrated and evaluated via simulations. An mRNA segment data set is used to illustrate and motivate the proposed sampling method.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312000953
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 8 ()
    Pages: 2562-2573

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:8:p:2562-2573
    DOI: 10.1016/j.csda.2012.02.013
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. Anne Chao & John Bunge, 2002. "Estimating the Number of Species in a Stochastic Abundance Model," Biometrics, The International Biometric Society, vol. 58(3), pages 531-539, 09.
    2. Ji-Ping Wang, 2010. "Estimating species richness by a Poisson-compound gamma model," Biometrika, Biometrika Trust, vol. 97(3), pages 727-740.
    3. 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.
    4. Mary C. Christman & Feng Lan, 2001. "Inverse Adaptive Cluster Sampling," Biometrics, The International Biometric Society, vol. 57(4), pages 1096-1105, December.
    5. Robert M. Dorazio & Bhramar Mukherjee & Li Zhang & Malay Ghosh & Howard L. Jelks & Frank Jordan, 2008. "Modeling Unobserved Sources of Heterogeneity in Animal Abundance Using a Dirichlet Process Prior," Biometrics, The International Biometric Society, vol. 64(2), pages 635-644, 06.
    6. Mao, Chang Xuan, 2006. "Inference on the Number of Species Through Geometric Lower Bounds," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1663-1670, December.
    7. Jeffrey S. Morris & Keith A. Baggerly & Kevin R. Coombes, 2003. "Bayesian Shrinkage Estimation of the Relative Abundance of mRNA Transcripts Using SAGE," Biometrics, The International Biometric Society, vol. 59(3), pages 476-486, 09.
    8. P. Besbeas & S. N. Freeman & B. J. T. Morgan & E. A. Catchpole, 2002. "Integrating Mark–Recapture–Recovery and Census Data to Estimate Animal Abundance and Demographic Parameters," Biometrics, The International Biometric Society, vol. 58(3), pages 540-547, 09.
    9. Hongmei Zhang, 2007. "Inferences on the Number of Unseen Species and the Number of Abundant/Rare Species," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(6), pages 725-740.
    10. Shirley Pledger & Kenneth H. Pollock & James L. Norris, 2003. "Open Capture-Recapture Models with Heterogeneity: I. Cormack-Jolly-Seber Model," Biometrics, The International Biometric Society, vol. 59(4), pages 786-794, December.
    11. Shirley Pledger & Kenneth H. Pollock & James L. Norris, 2010. "Open Capture–Recapture Models with Heterogeneity: II. Jolly–Seber Model," Biometrics, The International Biometric Society, vol. 66(3), pages 883-890, 09.
    12. Xuan Mao, Chang, 2007. "Estimating population sizes for capture-recapture sampling with binomial mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5211-5219, July.
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