• 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.

• The Journal of the Acoustical Society of Korea
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• v.34 no.3
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• pp.240-246
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• 2015

In this paper, speech enhancement using nonnegative matrix factorization with temporal continuity has been addressed. Speech and noise signals are modeled as Possion distributions, and basis vectors and gain vectors of NMF are modeled as Gamma distributions. Temporal continuity of the gain vector is known to be critical to the quality of enhanced speech signals. In this paper, temporal continiuty is implemented by adopting Gamma-Markov chain priors for noise gain vectors during the separation phase. Simulation results show that the Gamma-Markov chain models temporal continuity of noise signals and track changes in noise effectively.