We study different variants of the Gibbs sampler algorithm from the perspective of their applicability to the estimation of power spectra of the cosmic microwave background (CMB) anisotropies. We focus on approaches which aim at reducing the cost of a computationally heavy constrained realization step and capitalize on the interweaving strategy to ensure that our algorithms mix well for high and low signal-to-noise ratio components. In particular, we propose an approach, which we refer to as Centered overrelax, which avoids the constraint realization step completely at the cost of additional, auxiliary variables and the need for overrelaxation. We demonstrate these variants and compare their merits on full and cut sky simulations, quantifying their performance in terms of an effective sample size (ESS) per second. We find that on nearly full-sky, satellite-like data, the proposed Gibbs sampler with overrelaxation performs between one and two orders of magnitude better than the usual Gibbs sampler potentially providing an interesting alternative to the currently favored approaches.

翻译：我们从可适用于估计宇宙微波背景(CMB)血管血管电源光谱的角度研究Gibbs采样器算法的不同变方。我们侧重于旨在降低计算超重的实现步骤的成本并利用交织战略以确保我们的算法能够很好地混合高低信号对噪音比率的成分。我们特别建议了一种方法,我们称之为中度过度放纵,以额外辅助变量和过度松绑的必要性为代价,完全避免限制实现步骤。我们展示了这些变方,并比较了这些变方的全速和缩短天空模拟的优点,用有效的样品大小/秒来量化其性能。我们发现,在几乎完全的卫星类数据上,拟议的Gibbs采样器在高度松绑的一至两级之间运行,比通常的Gibbs采样器可能为目前偏好的方法提供一个有趣的替代方法。