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Canonical representation of conditionally specified multivariate discrete distributions

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  • Ip, Edward H.
  • Wang, Yuchung J.

Abstract

Most work on conditionally specified distributions has focused on approaches that operate on the probability space, and the constraints on the probability space often make the study of their properties challenging. We propose decomposing both the joint and conditional discrete distributions into characterizing sets of canonical interactions, and we prove that certain interactions of a joint distribution are shared with its conditional distributions. This invariance opens the door for checking the compatibility between conditional distributions involving the same set of variables. We formulate necessary and sufficient conditions for the existence and uniqueness of discrete conditional models, and we show how a joint distribution can be easily computed from the pool of interactions collected from the conditional distributions. Hence, the methods can be used to calculate the exact distribution of a Gibbs sampler. Furthermore, issues such as how near compatibility can be reconciled are also discussed. Using mixed parametrization, we show that the proposed approach is based on the canonical parameters, while the conventional approaches are based on the mean parameters. Our advantage is partly due to the invariance that holds only for the canonical parameters.

Suggested Citation

  • Ip, Edward H. & Wang, Yuchung J., 2009. "Canonical representation of conditionally specified multivariate discrete distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1282-1290, July.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:6:p:1282-1290
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    References listed on IDEAS

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    1. Donald B. Rubin, 2003. "Nested multiple imputation of NMES via partially incompatible MCMC," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(1), pages 3-18, February.
    2. Edward Ip & Yuchung Wang & Paul Boeck & Michel Meulders, 2004. "Locally dependent latent trait model for polytomous responses with application to inventory of hostility," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 191-216, June.
    3. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose Maria, 2002. "Exact and near compatibility of discrete conditional distributions," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 231-252, August.
    4. A. Gelman & T. P. Speed, 1999. "Corrigendum: Characterizing a joint probability distribution by conditionals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 483-483, April.
    5. Arnold, Barry C. & Castillo, Enrique & Sarabia, José María, 1996. "Specification of distributions by combinations of marginal and conditional distributions," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 153-157, February.
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    Cited by:

    1. Kuo, Kun-Lin & Song, Chwan-Chin & Jiang, Thomas J., 2017. "Exactly and almost compatible joint distributions for high-dimensional discrete conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 115-123.
    2. Wang, Yuchung J. & Kuo, Kun-Lin, 2010. "Compatibility of discrete conditional distributions with structural zeros," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 191-199, January.
    3. Kun-Lin Kuo & Yuchung J. Wang, 2023. "Analytical Computation of Pseudo-Gibbs Distributions for Dependency Networks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-17, March.
    4. Kuo, Kun-Lin & Wang, Yuchung J., 2011. "A simple algorithm for checking compatibility among discrete conditional distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2457-2462, August.
    5. Berti, Patrizia & Dreassi, Emanuela & Rigo, Pietro, 2014. "Compatibility results for conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 190-203.
    6. Chen, Shyh-Huei & Ip, Edward H. & Wang, Yuchung J., 2011. "Gibbs ensembles for nearly compatible and incompatible conditional models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1760-1769, April.
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    8. Dreassi, Emanuela & Rigo, Pietro, 2017. "A note on compatibility of conditional autoregressive models," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 9-16.
    9. Yao, Yi-Ching & Chen, Shih-chieh & Wang, Shao-Hsuan, 2014. "On compatibility of discrete full conditional distributions: A graphical representation approach," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 1-9.

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