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High-dimensional generation of Bernoulli random vectors

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  • Modarres, Reza

Abstract

The objective of this paper is to explore different modeling strategies to generate high-dimensional Bernoulli vectors. We discuss the multivariate Bernoulli (MB) distribution, probe its properties and examine three models for generating random vectors. A latent multivariate normal model whose bivariate distributions are approximated with Plackett distributions with univariate normal distributions is presented. A conditional mean model is examined where the conditional probability of success depends on previous history of successes. A mixture of beta distributions is also presented that expresses the probability of the MB vector as a product of correlated binary random variables. Each method has a domain of effectiveness. The latent model offers unpatterned correlation structures while the conditional mean and the mixture model provide computational feasibility for high-dimensional generation of MB vectors.

Suggested Citation

  • Modarres, Reza, 2011. "High-dimensional generation of Bernoulli random vectors," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1136-1142, August.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1136-1142
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    References listed on IDEAS

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    1. N. Rao Chaganty & Harry Joe, 2006. "Range of correlation matrices for dependent Bernoulli random variables," Biometrika, Biometrika Trust, vol. 93(1), pages 197-206, March.
    2. Bahjat F. Qaqish, 2003. "A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations," Biometrika, Biometrika Trust, vol. 90(2), pages 455-463, June.
    3. Farrell, Patrick J. & Sutradhar, Brajendra C., 2006. "A non-linear conditional probability model for generating correlated binary data," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 353-361, February.
    4. James, Barry & James, Kang & Qi, Yongcheng, 2008. "Limit theorems for correlated Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2339-2345, October.
    5. Patrick J. Farrell & Katrina Rogers-Stewart, 2008. "Methods for Generating Longitudinally Correlated Binary Data," International Statistical Review, International Statistical Institute, vol. 76(1), pages 28-38, April.
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    Cited by:

    1. Demirhan, Haydar & Kalaylioglu, Zeynep, 2015. "On the generalized multivariate Gumbel distribution," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 93-99.
    2. Modarres, Reza, 2014. "On the interpoint distances of Bernoulli vectors," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 215-222.
    3. repec:eee:reensy:v:133:y:2015:i:c:p:1-10 is not listed on IDEAS

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