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A flexible multivariate model for high-dimensional correlated count data

Author

Listed:
  • Alexander D. Knudson

    (University of Nevada)

  • Tomasz J. Kozubowski

    (University of Nevada)

  • Anna K. Panorska

    (University of Nevada)

  • A. Grant Schissler

    (University of Nevada)

Abstract

We propose a flexible multivariate stochastic model for over-dispersed count data. Our methodology is built upon mixed Poisson random vectors (Y1,…,Yd), where the {Yi} are conditionally independent Poisson random variables. The stochastic rates of the {Yi} are multivariate distributions with arbitrary non-negative margins linked by a copula function. We present basic properties of these mixed Poisson multivariate distributions and provide several examples. A particular case with geometric and negative binomial marginal distributions is studied in detail. We illustrate an application of our model by conducting a high-dimensional simulation motivated by RNA-sequencing data.

Suggested Citation

  • Alexander D. Knudson & Tomasz J. Kozubowski & Anna K. Panorska & A. Grant Schissler, 2021. "A flexible multivariate model for high-dimensional correlated count data," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-21, December.
    • Handle: RePEc:spr:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00119-y
    DOI: 10.1186/s40488-021-00119-y
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    References listed on IDEAS

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    3. Demirtas, Hakan & Hedeker, Donald, 2011. "A Practical Way for Computing Approximate Lower and Upper Correlation Bounds," The American Statistician, American Statistical Association, vol. 65(2), pages 104-109.
    4. Huifen Chen, 2001. "Initialization for NORTA: Generation of Random Vectors with Specified Marginals and Correlations," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 312-331, November.
    5. Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
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