混合个数未知的多元正态混合模型的贝叶斯推断
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摘要
文章研究了混合个数未知情况下的多元正态混合模型的贝叶斯推断。首先利用可逆跳MCMC算法,通过在可变维参数空间跳跃式抽样,实现贝叶斯模型选择的目的。根据后验概率确定混合个数之后再用MCMC算法对模型的其他参数进行贝叶斯估计。提出了利用Cholesky分裂原理对协方差矩阵进行分裂和合并,满足可逆跳算法对参数分裂和合并的所有要求,还满足了分裂和合并过程中协方差矩阵必须正定这一特殊要求。
This paper studies the Bayesian inference of the multivariate normal mixed model with unknown number of mixtures.Firstly,the paper uses the reversible MCMC algorithm to realize the selection of Bayesian model by skip sampling in variable dimensional parameter space.And then the MCMC algorithm is employed to estimate the other parameters of the model after determining the number of mixtures according to posterior probability.Finally the paper proposes to use Cholesky decomposition principle to split and merge the covariance matrix,so as to satisfy all the requirements of parameter splitting and merging in reversible jump algorithm,and also satisfies the special requirement that the covariance matrix must be positive definite in the process of splitting and merging.
This paper studies the Bayesian inference of the multivariate normal mixed model with unknown number of mixtures.Firstly,the paper uses the reversible MCMC algorithm to realize the selection of Bayesian model by skip sampling in variable dimensional parameter space.And then the MCMC algorithm is employed to estimate the other parameters of the model after determining the number of mixtures according to posterior probability.Finally the paper proposes to use Cholesky decomposition principle to split and merge the covariance matrix,so as to satisfy all the requirements of parameter splitting and merging in reversible jump algorithm,and also satisfies the special requirement that the covariance matrix must be positive definite in the process of splitting and merging.
引文
[1]张香云,宋红凤.基于Gibbs抽样正态混合模型的参数估计[J].统计与决策,2014,9(5).
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[8]茆诗松.贝叶斯统计[M].北京:中国统计出版社,1999.
[9]韦博成.参数统计教程[M].北京:高等教育出版社,2006.
[10]Lee S Y,Song X Y.Bayesian Model Selection for Mixture of Structure Equation Models With an Unknown Number of Components[J].British Journal of Mathematical and Statistical Psychology,2003,56(1)./
[2]蔡鸣晶.正态混合模型的Bayes分析[J].江苏经贸职业技术学院学报,2009,1(12).
[3]尤芳.混合模型的参数估计[D].苏州:苏州大学学位论文,2006.
[4]Richardson S,Green P J.On Bayesian Analysis of Mixtures With an Unknown Number of Components(With Discussion)[J].Journal of the Royal Statistical Society,Series B,1997,59(4).
[5]茆诗松,王静龙,濮晓龙.高等数理统计[M].北京:高等教育出版社,2012.
[6]Green P J.Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination[J].Biometrika,1995,82(4).
[7]Robert C P,Ryden T,Titterington D M.Bayesian Inference in Hidden Markov Models Through the Reversible Jump Markov Chain Monte Carlo Method[J].Journal of the Royal Statistical Society,Series B,2000,62(1).
[8]茆诗松.贝叶斯统计[M].北京:中国统计出版社,1999.
[9]韦博成.参数统计教程[M].北京:高等教育出版社,2006.
[10]Lee S Y,Song X Y.Bayesian Model Selection for Mixture of Structure Equation Models With an Unknown Number of Components[J].British Journal of Mathematical and Statistical Psychology,2003,56(1)./