BeyondPlanck II. 通过 Gibbs 采样的 CMB 制图
BeyondPlanck II. CMB map-making through Gibbs sampling
AI总结：
本文提出一种用于CMB制图的Gibbs采样方法，将去条纹问题拆分为噪声滤波和地图分箱两步以大幅降低计算成本，并能高效处理数据间隙与残余噪声。该方法为BeyondPlanck端到端贝叶斯分析框架提供了具有严格误差传播和系统误差校正能力的制图基础。
摘要：
我们提出了一种用于 CMB 测量的制图问题的 Gibbs 采样解决方案，该方案建立在现有的去条纹方法之上。Gibbs 采样将计算量大的去条纹问题分为两个独立步骤：噪声滤波和地图分箱。作为两个独立步骤，两者的计算成本都比求解组合问题低得多。与与传统方法相比，这提供了巨大的性能优势，并使我们首次能够将去条纹基线长度降至单个样本。。我们将 Gibbs 程序应用于模拟的 Planck 30 GHz 数据。我们发现，时间序列数据中的间隙可以通过在 Gibbs 过程中用模拟噪声进行填补而得到高效处理。Gibbs 程序产生一条地图样本链，我们从中可以计算后验均值作为最佳估计地图。链中的变化提供了关于相关残余噪声的信息，而无需构建完整的噪声协方差矩阵。然而，如果只需要单个最大似然频率图估计，我们发现传统共轭梯度求解器在总迭代次数方面比 Gibbs 采样器收敛快得多。Gibbs 采样方法的概念优势在于统计上定义良好的误差传播和系统误差校正，该方法构成了 BeyondPlanck 框架中所用制图算法的概念基础，该框架实现了首个针对 CMB 观测的端到端贝叶斯分析流水线。
英文摘要：
We present a Gibbs sampling solution to the map-making problem for CMB measurements, building on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem into two separate steps; noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods, and allows us for the first time to bring the destriping baseline length to a single sample. We apply the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we may compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction, and this methodology forms the conceptual basis for the map-making algorithm employed in the BeyondPlanck framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.
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