Gao Xu, Shen Weining, Shahbaba Babak, Fortin Norbert J, Ombao Hernando
Department of Statistics, University of California, Irvine, California, U.S.A.
Department of Neurobiology and Behavior, University of California Irvine, Irvine, California, U.S.A.
Stat Sin. 2020 Jul;30(3):1561-1582. doi: 10.5705/ss.202017.0420.
We propose an evolutionary state space model (E-SSM) for analyzing high dimensional brain signals whose statistical properties evolve over the course of a non-spatial memory experiment. Under E-SSM, brain signals are modeled as mixtures of components (e.g., AR(2) process) with oscillatory activity at pre-defined frequency bands. To account for the potential non-stationarity of these components (since the brain responses could vary throughout the entire experiment), the parameters are allowed to vary over epochs. Compared with classical approaches such as independent component analysis and filtering, the proposed method accounts for the entire temporal correlation of the components and accommodates non-stationarity. For inference purpose, we propose a novel computational algorithm based upon using Kalman smoother, maximum likelihood and blocked resampling. The E-SSM model is applied to simulation studies and an application to a multi-epoch local field potentials (LFP) signal data collected from a non-spatial (olfactory) sequence memory task study. The results confirm that our method captures the evolution of the power for different components across different phases in the experiment and identifies clusters of electrodes that behave similarly with respect to the decomposition of different sources. These findings suggest that the activity of different electrodes does change over the course of an experiment in practice; treating these epoch recordings as realizations of an identical process could lead to misleading results. In summary, the proposed method underscores the importance of capturing the evolution in brain responses over the study period.
我们提出了一种进化状态空间模型（E-SSM），用于分析高维脑信号，这些脑信号的统计特性在非空间记忆实验过程中会发生演变。在E-SSM模型下，脑信号被建模为具有预定义频段振荡活动的成分混合（例如，AR(2)过程）。为了考虑这些成分可能的非平稳性（因为大脑反应在整个实验过程中可能会有所不同），允许参数在各个时期发生变化。与独立成分分析和滤波等经典方法相比，所提出的方法考虑了成分的整个时间相关性，并适应了非平稳性。出于推断目的，我们提出了一种基于卡尔曼平滑器、最大似然和分组重采样的新型计算算法。E-SSM模型应用于模拟研究，并应用于从非空间（嗅觉）序列记忆任务研究中收集的多时期局部场电位（LFP）信号数据。结果证实，我们的方法捕捉了实验中不同阶段不同成分功率的演变，并识别出在不同源分解方面表现相似的电极簇。这些发现表明，在实际实验过程中，不同电极的活动确实会发生变化；将这些时期记录视为相同过程的实现可能会导致误导性结果。总之，所提出的方法强调了在研究期间捕捉大脑反应演变的重要性。
