Spectral Decompositions of Multiple Time Series: A Bayesian Non-parametric Approach
Spectral Decompositions of Multiple Time Series: A Bayesian Non-parametric Approach
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DOI：
10.1007/s11336-013-9354-0
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发表时间：
2014-01-01
期刊：
影响因子：
3
通讯作者：
Prado, Raquel
中科院分区：
文献类型：
--
作者：
Macaro, Christian;Prado, Raquel
我们考虑多个时间序列的谱分解，在研究中出现的兴趣在于评估两个或多个因素的影响。我们将每个时间序列的谱密度写为与不同水平的因子相关的谱密度之和。然后，我们使用惠特尔的近似的似然函数，并遵循贝叶斯非参数的方法来获得后验推断的频谱密度的基础上伯恩斯坦-狄利克雷先验分布。先验知识具有重要的战略意义，因为它为模型提供了可识别性条件，并允许我们量化对这些条件的置信度。本文提出了一种用于这类频域模型后验推断的马尔可夫链蒙特卡罗（MCMC）算法，并通过分析单路和双路谱模型的模拟数据和真实的数据来说明这种方法。特别是，我们提出了一个分析功能性磁共振成像（fMRI）的大脑反应，在个人参与了一个设计的实验，以研究人类的疼痛感知。
We consider spectral decompositions of multiple time series that arise in studies where the interest lies in assessing the influence of two or more factors. We write the spectral density of each time series as a sum of the spectral densities associated to the different levels of the factors. We then use Whittle's approximation to the likelihood function and follow a Bayesian non-parametric approach to obtain posterior inference on the spectral densities based on Bernstein-Dirichlet prior distributions. The prior is strategically important as it carries identifiability conditions for the models and allows us to quantify our degree of confidence in such conditions. A Markov chain Monte Carlo (MCMC) algorithm for posterior inference within this class of frequency-domain models is presented.We illustrate the approach by analyzing simulated and real data via spectral one-way and two-way models. In particular, we present an analysis of functional magnetic resonance imaging (fMRI) brain responses measured in individuals who participated in a designed experiment to study pain perception in humans.