Survey-based measurements of the spectral energy distributions (SEDs) of galaxies have flux density estimates on badly misaligned grids in rest-frame wavelength. The shift to rest frame wavelength also causes estimated SEDs to have differing support. For many galaxies, there are sizeable wavelength regions with missing data. Finally, dim galaxies dominate typical samples and have noisy SED measurements, many near the limiting signal-to-noise level of the survey. These limitations of SED measurements shifted to the rest frame complicate downstream analysis tasks, particularly tasks requiring computation of functionals (e.g., weighted integrals) of the SEDs, such as synthetic photometry, quantifying SED similarity, and using SED measurements for photometric redshift estimation. We describe a hierarchical Bayesian framework, drawing on tools from functional data analysis, that models SEDs as a random superposition of smooth continuum basis functions (B-splines) and line features, comprising a finite-rank, nonstationary Gaussian process, measured with additive Gaussian noise. We apply this *Splines 'n Lines* (SnL) model to a collection of 678,239 galaxy SED measurements comprising the Main Galaxy Sample from the Sloan Digital Sky Survey, Data Release 17, demonstrating capability to provide continuous estimated SEDs that reliably denoise, interpolate, and extrapolate, with quantified uncertainty, including the ability to predict line features where there is missing data by leveraging correlations between line features and the entire continuum.

翻译：基于巡天的星系光谱能量分布（SED）测量在静止框架波长上存在严重错位的通量密度估计网格。静止框架波长的转换也导致估计的SED支撑集不同。对于许多星系，存在具有显著缺失数据的波长区域。最后，暗弱星系主导典型样本，其SED测量噪声较大，许多接近巡天信噪比极限。这些静止框架SED测量的局限性使下游分析任务复杂化，特别是需要计算SED泛函（如加权积分）的任务，例如合成测光、量化SED相似性以及利用SED测量进行测光红移估计。我们描述了一个分层贝叶斯框架，利用函数数据分析工具，将SED建模为平滑连续基函数（B样条）和谱线特征的随机叠加，构成一个有限秩非平稳高斯过程，并以加性高斯噪声进行测量。我们将此样条与谱线（SnL）模型应用于斯隆数字巡天第17批数据发布的主星系样本中678,239个星系的SED测量，展示了该模型能够提供连续的估计SED，在量化不确定性的情况下可靠地降噪、插值和外推，包括通过利用谱线特征与连续谱之间的相关性预测缺失数据处的谱线特征的能力。