We develop a new methodology for determining the location and dynamics of brain activity from combined magnetoencephalography (MEG) and electroencephalography (EEG) data. The resulting inverse problem is ill‐posed and is one of the most difficult problems in neuroimaging data analysis. In our development we propose a solution that combines the data from three different modalities, magnetic resonance imaging (MRI), MEG and EEG, together. We propose a new Bayesian spatial finite mixture model that builds on the mesostate‐space model developed by Daunizeau & Friston [Daunizeau and Friston, NeuroImage 2007; 38, 67–81]. Our new model incorporates two major extensions: (i) We combine EEG and MEG data together and formulate a joint model for dealing with the two modalities simultaneously; (ii) we incorporate the Potts model to represent the spatial dependence in an allocation process that partitions the cortical surface into a small number of latent states termed mesostates. The cortical surface is obtained from MRI. We formulate the new spatiotemporal model and derive an efficient procedure for simultaneous point estimation and model selection based on the iterated conditional modes algorithm combined with local polynomial smoothing. The proposed method results in a novel estimator for the number of mixture components and is able to select active brain regions, which correspond to active variables in a high‐dimensional dynamic linear model. The methodology is investigated using synthetic data and simulation studies and then demonstrated on an application examining the neural response to the perception of scrambled faces. R software implementing the methodology along with several sample datasets are available at the following GitHub repository https://github.com/v2south/PottsMix. The Canadian Journal of Statistics 47: 688–711; 2019 © 2019 Statistical Society of Canada

中文翻译：

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脑磁图和脑电图数据结合的Potts-mixture时空联合模型

我们开发了一种新的方法，用于从结合磁脑电图（MEG）和脑电图（EEG）数据确定大脑活动的位置和动态。由此产生的逆问题是不适的，并且是神经影像数据分析中最困难的问题之一。在我们的开发中，我们提出了一种解决方案，将来自三种不同模态的数据（磁共振成像（MRI），MEG和EEG）组合在一起。我们提出了一个新的贝叶斯空间有限混合模型，该模型建立在Daunizeau和Friston [Daunizeau和Friston，NeuroImage 2007; 38，67–81]。我们的新模型包括两个主要扩展：（i）我们将EEG和MEG数据结合在一起，并制定了一个同时处理这两种模式的联合模型；（ii）我们结合Potts模型来表示分配过程中的空间依赖性，该分配过程将皮层表面划分为少量称为中间态的潜伏状态。皮质表面是从MRI获得的。我们制定了新的时空模型，并基于迭代条件模式算法与局部多项式平滑相结合，导出了同时进行点估计和模型选择的有效程序。所提出的方法为混合成分的数量提供了一种新颖的估计器，并且能够选择活跃的大脑区域，该区域对应于高维动态线性模型中的活跃变量。使用合成数据和模拟研究对方法进行了研究，然后在检查神经系统对加扰脸部感知的神经反应的应用中进行了演示。《加拿大统计杂志》 47：688–711；2019©2019加拿大统计学会