  The Markov chain Monte Carlo update method to construct an irreversible
kernel has been reviewed and extended to general state spaces. The several
convergence conditions of the Markov chain were discussed. The alternative
methods to the Gibbs sampler and the Metropolis-Hastings algorithm were
proposed and assessed in some models. The distribution convergence and the
sampling efficiency are significantly improved in the Potts model, the
bivariate Gaussian model, and so on. This approach using the irreversible
kernel can be applied to any Markov chain Monte Carlo sampling and it is
expected to improve the efficiency in general.
