低信噪比CMB数据分析的马尔可夫链蒙特卡罗算法
A Markov Chain Monte Carlo Algorithm for analysis of low signal-to-noise CMB data
摘要：
我们提出了一种新的蒙特卡罗马尔可夫链算法的CMB分析在低信噪比制度。该方法是对原有CMB Gibbs采样器的补充和改进，有效地解决了直接Gibbs采样器信噪比低的问题。新算法是一个简单的Metropolis-Hastings采样器，具有用于功率谱C_1的一般建议规则，随后是天空信号的特定确定性重标度操作。这种联合移动的接受概率仅通过原始天空样本和建议天空样本之间的卡方差而取决于天空地图，这在低信噪比状态下接近于1。该算法通过将该移动与标准吉布斯移动交替来完成。总之，这两个建议构成了一个计算效率高的算法，用于映射出完整的联合CMB后，无论是在高和低信噪比制度。
英文摘要：
We present a new Monte Carlo Markov Chain algorithm for CMB analysis in the low signal-to-noise regime. This method builds on and complements the previously described CMB Gibbs sampler, and effectively solves the low signal-to-noise inefficiency problem of the direct Gibbs sampler. The new algorithm is a simple Metropolis-Hastings sampler with a general proposal rule for the power spectrum, C_l, followed by a particular deterministic rescaling operation of the sky signal. The acceptance probability for this joint move depends on the sky map only through the difference of chi-squared between the original and proposed sky sample, which is close to unity in the low signal-to-noise regime. The algorithm is completed by alternating this move with a standard Gibbs move. Together, these two proposals constitute a computationally efficient algorithm for mapping out the full joint CMB posterior, both in the high and low signal-to-noise regimes.
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