This paper proposes a generalization of Gaussian mixture models, where the mixture weight is allowed to behave as an unknown function of time. This model is capable of successfully capturing the features of the data, as demonstrated by simulated and real datasets. It can be useful in studies such as clustering, change-point and process control. In order to estimate the mixture weight function, we propose two new Bayesian nonlinear dynamic approaches for polynomial models, that can be extended to other problems involving polynomial nonlinear dynamic models. One of the methods, called here component-wise Metropolis-Hastings, apply the Metropolis-Hastings algorithm to each local level component of the state equation. It is more general and can be used in any situation where the observation and state equations are nonlinearly connected. The other method tends to be faster, but is applied specifically to binary data (using the probit link function). The performance of these methods of estimation, in the context of the proposed dynamic Gaussian mixture model, is evaluated through simulated datasets. Also, an application to an array Comparative Genomic Hybridization (aCGH) dataset from glioblastoma cancer illustrates our proposal, highlighting the ability of the method to detect chromosome aberrations.
翻译:本文建议对高斯混合物模型进行概括化, 允许混合重量作为未知的时间函数。 该模型能够成功地捕捉数据特征, 模拟和真实的数据集证明了这一点。 它可以在集群、 变化点和进程控制等研究中有用。 为了估计混合重量函数, 我们建议两种新的巴耶西亚非线性多元模型的非线性动态方法, 这些方法可以扩展至涉及多边非线性动态模型的其他问题。 其中一种方法, 称为Metropolis- Hasting, 能够成功地捕捉数据特征, 通过模拟数据集将Metropolips- Hasting 算法应用到状态方程式的每个本地级组件。 它比较笼统, 可以在观测和状态方程式不线性连接的任何情况下使用。 另一种方法倾向于更快, 但具体应用到二元数据( 使用 probit 链接功能) 。 在拟议的动态高斯混合模型中, 通过模拟数据集评估这些方法的性能。 另外, 一种应用Metopolipolips- Has 算法, 演示我们测算方法的对比性模型。