Perfect sampling on 2×⋯×2×K contingency tables with an application to SAGE data

The perfect sampling method of Kijima and Matsui (2006) for 2×K contingency tables is extended to 2×⋯×2×K tables. Based on this, a Metropolis sampling method is then proposed to implement Zelen's homogeneity test. Finally, an application is shown on gene expression data where cancer samples are compared to non-cancer samples across various tissues.