Beyond Whittle: Nonparametric Correction of a Parametric Likelihood with a Focus on Bayesian Time Series Analysis
Beyond Whittle: Nonparametric Correction of a Parametric Likelihood with a Focus on Bayesian Time Series Analysis
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DOI：
10.1214/18-ba1126
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发表时间：
2019-12-01
影响因子：
4.4
通讯作者：
Meyer, Renate
中科院分区：
文献类型：
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作者：
Kirch, Claudia;Edwards, Matthew C.;Meyer, Renate
非参数贝叶斯推理在过去十年中得到了快速发展，但只有少数非参数贝叶斯时间序列分析方法得到了发展。大多数现有的方法使用惠特尔的似然贝叶斯建模的谱密度作为平稳时间序列的主要非参数特征。众所周知，使用惠特尔的可能性的效率损失可能是相当大的。另一方面，如果观察到的时间序列接近所考虑的模型类，参数方法比非参数方法更强大，但如果模型被错误指定，则会失败。因此，我们建议一个参数似然的非参数校正，利用参数模型的效率，同时通过非参数修正降低敏感性。我们使用一个非参数伯恩斯坦多项式先验的谱密度与权重的Dirichlet过程，并证明了高斯平稳时间序列的后验一致性。贝叶斯后验计算通过MH内吉布斯采样器和非参数校正的似然高斯时间序列的性能进行了说明，在模拟研究和三个天文学应用，包括估计的光谱密度的引力波数据从先进的激光干涉引力波天文台（LIGO）。
Nonparametric Bayesian inference has seen a rapid growth over the last decade but only few nonparametric Bayesian approaches to time series analysis have been developed. Most existing approaches use Whittle's likelihood for Bayesian modelling of the spectral density as the main nonparametric characteristic of stationary time series. It is known that the loss of efficiency using Whittle's likelihood can be substantial. On the other hand, parametric methods are more powerful than nonparametric methods if the observed time series is close to the considered model class but fail if the model is misspecified. Therefore, we suggest a nonparametric correction of a parametric likelihood that takes advantage of the efficiency of parametric models while mitigating sensitivities through a nonparametric amendment. We use a nonparametric Bernstein polynomial prior on the spectral density with weights induced by a Dirichlet process and prove posterior consistency for Gaussian stationary time series. Bayesian posterior computations are implemented via an MH-within-Gibbs sampler and the performance of the nonparametrically corrected likelihood for Gaussian time series is illustrated in a simulation study and in three astronomy applications, including estimating the spectral density of gravitational wave data from the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO).