Bayesian nonparametric methods for spectral analysis of complex brain signals

复杂的多重时间序列经常被记录在几个应用研究领域，如神经科学、环境计量学和计量经济学。本项目发展贝叶斯非参数方法及相关计算工具，用于多时间序列的频域分析。特别是，本项目将开发的统计方法是由分析临床和非临床研究中记录的脑信号的需要所驱动的，包括脑电图、功能磁共振成像数据和脑磁图。采用一种新颖灵活的混合建模框架来表示多时间序列的光谱特征。计算效率高的算法将被实现、测试并用于分析复杂和大维度的大脑信号。这些算法将利用各种计算方法在贝叶斯非参数模型中进行推理。将开发的模型和方法具有以下主要特点：(i)它们将提供多个信号的谱密度的灵活表示以及计算可行性；（ii）它们将允许研究人员研究具有相似谱特征的多个时间序列的聚类模式；（iii）它们将纳入分层设置，可以适当地容纳涉及多个试验、多个受试者和/或相关协变量的神经科学数据集。该研究项目有可能影响需要分析几个复杂大脑信号的数据密集型神经科学研究。

Complex multiple time series are often recorded in several applied areas of research such as neuroscience, environmetrics, and econometrics. This project develops Bayesian nonparametric methods and related computational tools for frequency-domain analysis of multiple time series. In particular, the statistical approaches that will be developed in this project are motivated by the need to analyze brain signals recorded in clinical and non-clinical studies including electroencephalograms, fMRI data, and magnetoencephalograms.A novel and flexible mixture modeling framework will be used to represent the spectral characteristics of multiple time series. Computationally efficient algorithms will be implemented, tested and used to analyze complex and large-dimensional brain signals. These algorithms will make use of a variety of computational methods for inference in Bayesian nonparametric models. The models and methods that will be developed have the following key features: (i) they will provide flexible representations of the spectral densities of multiple signals as well as computational feasibility (ii) they will allow researchers to investigate clustering patterns of multiple time series with similar spectral characteristics, and (iii) they will incorporate hierarchical settings that can appropriately accommodate neuroscience data sets involving multiple trials, multiple subjects and/or relevant covariates. The research project has the potential of impacting data-intensive neuroscience research that requires the analysis of several complex brain signals.