Abstract Various approaches for spectral analysis based on regularly spaced data have already been well-established, but the spectral inference based on irregularly spaced data are still essentially limited. Under the Bayesian framework, a detouring approach for spectral estimation is proposed for analyzing irregularly spaced data. The detouring process is accomplished by three steps: (1) normalizing the data in some sense on frequency domain by a time-scale change, (2) estimating the spectral density of the time-scale changed process, and (3) solving the estimated spectrum by the relation of spectral densities between the model and its time-scale-changed version. The proposed approach uses a Hamiltonian Monte Carlo—within Gibbs technique to fit smoothing splines to the periodogram. Our technique produces an automatically smoothed spectral estimate. The time-scale-change not only allows basis functions in the smoothing splines to be independent of sampling design, but also makes the proposed estimation need not to adjust tuning parameters according to different irregularly spaced data.

中文翻译：

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基于不规则间隔数据的谱密度非参数贝叶斯推理

摘要 各种基于规则间隔数据的光谱分析方法已经成熟，但基于不规则间隔数据的光谱推断仍然存在本质上的局限性。在贝叶斯框架下，提出了一种谱估计的迂回方法来分析不规则间隔的数据。迂回过程通过三个步骤完成：（1）通过时标变化在频域上对某种意义上的数据进行归一化，（2）估计时标变化过程的频谱密度，以及（3）求解估计的光谱通过模型与其时标变化版本之间的光谱密度的关系。建议的方法使用哈密顿蒙特卡罗——在 Gibbs 技术中将平滑样条拟合到周期图。我们的技术产生一个自动平滑的频谱估计。时间尺度变化不仅允许平滑样条中的基函数独立于采样设计，而且使得所提出的估计不需要根据不同的不规则间隔数据调整调谐参数。