• KIISE Transactions on Computing Practices
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• v.21 no.1
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• pp.94-99
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• 2015

With the recent machine learning paradigm of using nonparametric Bayesian statistics and statistical inference based on random sampling, the Dirichlet distribution finds many uses in a variety of graphical models. It is a multivariate generalization of the gamma distribution and is defined on a continuous (K-1)-simplex. This paper presents a sampling method for a Dirichlet distribution for the problem of dividing an integer X into a sequence of K integers which sum to X. The target samples in our problem are all positive integer vectors when multiplied by a given X. They must be sampled from the correspondingly gridded simplex. In this paper we develop a Markov Chain Monte Carlo (MCMC) proposal distribution for the neighborhood grid points on the simplex and then present the complete algorithm based on the Metropolis-Hastings algorithm. The proposed algorithm can be used for the Markov model, HMM, and Semi-Markov model for accurate state-duration modeling. It can also be used for the Gamma-Dirichlet HMM to model q the global-local duration distributions.