In this paper we consider a Gaussian mixture model where the mixture weight behaves as an unknown function of time. To estimate the mixture weight function, we develop a Bayesian nonlinear dynamic approach for polynomial models. Two estimation methods that can be extended to other situations are considered. One of them, called here component-wise Metropolis-Hastings, is more general and can be used for any situation where the observation and state equations are nonlinearly connected. The other method tends to be faster but must be applied specifically to binary data (by using a probit link function). This kind of Gaussian mixture model is capable of successfully capturing the features of the data, as observed in numerical studies. It can be useful in studies such as clustering, change-point and process control. We apply the proposed method an array Comparative Genomic Hybridization (aCGH) dataset from glioblastoma cancer studies, where we illustrate the ability of the new method to detect chromosome aberrations.

翻译：在本文中,我们考虑的是一种高斯混合混合物模型,其中混合物的重量表现为未知的时间函数。为了估计混合物的重量函数,我们为多元模型制定了一种巴伊西亚非线性动态方法。考虑的是两种可以推广到其他情况的估算方法。其中一种方法叫作“部分-大都会-哈斯廷”,比较一般,可用于观测和状态方程非线性连接的任何情况。另一种方法倾向于更快,但必须具体应用于二进制数据(通过使用一种 probit 链接函数)。这种高斯混合模型能够成功地捕捉到数据特征,正如数字研究所观察到的那样。它可以在集群、改变点和过程控制等研究中有用。我们采用了一种拟议方法,即从Globblastoma癌症研究中比较基因混合(aCGH)数据集的阵列,我们在这里可以说明新的方法探测染色体畸变的能力。