Hybrid Methods for Running MCMC over I× J× K Contingency Tables
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We consider an I × J× K table with cell counts X_ijk≥ 0 for i = 1, … , I, j = 1, … , J and k = 1, … , K under the no-three-way interaction model. In this paper, we propose a Markov Chain Monte Carlo (MCMC) scheme connecting the set of all contingency tables by all basic moves of 2 × 2 × 2 minors with allowing X_ijk≥ -1 combined with simulated annealing. In addition, we propose a hybrid scheme of MCMC with basic moves by allowing -1 in cell counts combined with simulated annealing and Hit and Run (HAR) algorithm proposed by Andersen and Diaconis in order to improve a mixing time. We also compare this hybrid scheme with a hybrid method of sequential importance sampling (SIS) and MCMC introduced by Kahle, Yoshida, and Garcia-Puente. We apply these hybrid schemes to simulated and empirical data on Naval officer and enlisted population.
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