混合个数未知的多元正态混合模型的贝叶斯推断

Bayesian Inference for Multivariate Normal Mixed Model With Unknown Number of Mixtures

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.