分析脑电活动的标准方法是检查谱密度函数（SDF）并识别对信号的总体方差具有最大相对贡献的预定义频带。然而，这种方法的局限性在于振荡的精确频率和带宽随认知需求而变化。因此，它们不应该在实验中被任意地先验地定义。在本文中，我们开发了一种数据驱动的方法，该方法可以识别（i）显著峰值的数量，（ii）频率峰值的位置，以及（iii）它们相应的带宽（或峰值周围的功率分布）。我们提出了一种贝叶斯混合自回归分解方法（BMARD），它表示标准化的SDF作为一个Dirichlet过程的混合物的基础上的内核来自二阶自回归过程，完全表征的位置（峰值）和规模（带宽）参数。我们提出了一个Metropolis-Hastings within Gibbs算法，从混合参数的后验分布中进行采样。仿真研究证明了BMARD方法的鲁棒性和性能。最后，我们使用建议的BMARD方法来分析局部场电位（LFP）的活动，从实验室大鼠海马在不同的条件下，在非空间序列记忆实验，以确定最有趣的频带和检查之间的联系的特定模式的活动和审判特定的认知需求。
英文摘要：
The standard approach to analyzing brain electrical activity is to examine the spectral density function (SDF) and identify predefined frequency bands that have the most substantial relative contributions to the overall variance of the signal. However, a limitation of this approach is that the precise frequency and bandwidth of oscillations vary with cognitive demands. Thus they should not be arbitrarily defined a priori in an experiment. In this paper, we develop a data-driven approach that identifies (i) the number of prominent peaks, (ii) the frequency peak locations, and (iii) their corresponding bandwidths (or spread of power around the peaks). We propose a Bayesian mixture auto-regressive decomposition method (BMARD), which represents the standardized SDFas a Dirichlet process mixture based on a kernel derived from second-order auto-regressive processes which completely characterize the location (peak)and scale (bandwidth) parameters. We present a Metropolis-Hastings within Gibbs algorithm to sample from the posterior distribution of the mixture parameters. Simulation studies demonstrate the robustness and performance of the BMARD method. Finally, we use the proposed BMARD method to analyze local field potential (LFP) activity from the hippocampus of laboratory rats across different conditions in a non-spatial sequence memory experiment to identify the most interesting frequency bands and examine the link between specific patterns of activity and trial-specific cognitive demands.
Bayesian Varying-Effects Vector Autoregressive Models for Inference of Brain Connectivity Networks and Covariate Effects in Pediatric Traumatic Brain Injury
A Robbins-Monro algorithm for non-parametric estimation of NAR process with Markov-Switching: asymptotic normality
Aix-Marseille University（艾克斯-马赛大学）；Escuela de Matemáticas, Facultad de Ciencias, Universidad Central de Venezuela（委内瑞拉中央大学理学院数学系）；Departamento de Matemáticas, FACYT, Universidad de Carabobo（卡拉沃博大学FACYT数学系）
