Comparisons of three approaches for discrete conditional models

TY - JOUR

T1 - Comparisons of three approaches for discrete conditional models

AU - Wang, Yuchung J.

PY - 2012/1

Y1 - 2012/1

N2 - This article describes three methods for computing a discrete joint density from full conditional densities. They are the Gibbs sampler, a hybrid method, and an interaction-based method. The hybrid method uses the iterative proportional fitting algorithm, and it is derived from the mixed parameterization of a contingency table. The interaction-based approach is derived from the canonical parameters, while the Gibbs sampler can be regarded as based on the mean parameters. In short, different approaches are motivated by different parameterizations. The setting of a bivariate conditionally specified distribution is used as the premise for comparing the numerical accuracy of the three methods. Detailed comparisons of marginal distributions, odds ratios and expected values are reported. We give theoretical justifications as to why the hybrid method produces better approximation than the Gibbs sampler. Generalizations to more than two variables are discussed. In practice, Gibbs sampler has certain advantages: it is conceptually easy to understand and there are many software tools available. Nevertheless, the hybrid method and the interaction-based method are accurate and simple alternatives when the Gibbs sampler results in a slowly mixing chain and requires substantial simulation efforts.

AB - This article describes three methods for computing a discrete joint density from full conditional densities. They are the Gibbs sampler, a hybrid method, and an interaction-based method. The hybrid method uses the iterative proportional fitting algorithm, and it is derived from the mixed parameterization of a contingency table. The interaction-based approach is derived from the canonical parameters, while the Gibbs sampler can be regarded as based on the mean parameters. In short, different approaches are motivated by different parameterizations. The setting of a bivariate conditionally specified distribution is used as the premise for comparing the numerical accuracy of the three methods. Detailed comparisons of marginal distributions, odds ratios and expected values are reported. We give theoretical justifications as to why the hybrid method produces better approximation than the Gibbs sampler. Generalizations to more than two variables are discussed. In practice, Gibbs sampler has certain advantages: it is conceptually easy to understand and there are many software tools available. Nevertheless, the hybrid method and the interaction-based method are accurate and simple alternatives when the Gibbs sampler results in a slowly mixing chain and requires substantial simulation efforts.

KW - Characterizing set of interactions

KW - Full conditionals

KW - Gibbs Sampler

KW - Invariant interaction

KW - Odds ratio

KW - Parameterization

KW - Recurrent marginal measure

KW - Transition density

UR - https://www.scopus.com/pages/publications/80052324095

UR - https://www.scopus.com/pages/publications/80052324095#tab=citedBy

U2 - 10.1080/03610918.2011.579364

DO - 10.1080/03610918.2011.579364

M3 - Article

SN - 0361-0918

VL - 41

SP - 32

EP - 43

JO - Communications in Statistics: Simulation and Computation

JF - Communications in Statistics: Simulation and Computation

IS - 1

ER -