High-dimensional generation of Bernoulli random vectors
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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Volume (Year): 81 (2011)
Issue (Month): 8 (August)
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- 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, 04.
- 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.
- 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.
- 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.
- 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.
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