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High-dimensional generation of Bernoulli random vectors

Listed author(s):
  • Modarres, Reza
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    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.

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 81 (2011)
    Issue (Month): 8 (August)
    Pages: 1136-1142

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    Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1136-1142
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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. 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.
    3. 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.
    4. 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.
    5. 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.
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