论文标题
贝叶斯证据驱动的可能性选择天空平均21厘米信号提取
Bayesian evidence-driven likelihood selection for sky-averaged 21-cm signal extraction
论文作者
论文摘要
我们证明，贝叶斯证据可用于找到数据集的地面真相可能性功能的良好近似，这是无可能推理（LFI）范式的目标。作为一个具体的例子，我们使用了向前建模的21厘米信号天线温度数据集，我们在其中人为地注入了各种物理动机形式的噪声结构。我们发现，当噪声分布偏离高斯病例时，高斯的可能性效果很差，例如异质的辐射射线仪或重尾噪声。对于这些非高斯噪声结构，我们表明，普遍的正常可能性在类似的贝叶斯证据量表上，与我们注入的噪声的地面真相可能性功能相比，天空平均21厘米的信号恢复。因此，如果噪声结构是未知的，我们将广义的正常可能性函数作为真实可能性函数的良好近似。
We demonstrate that the Bayesian evidence can be used to find a good approximation of the ground truth likelihood function of a dataset, a goal of the likelihood-free inference (LFI) paradigm. As a concrete example, we use forward modelled sky-averaged 21-cm signal antenna temperature datasets where we artificially inject noise structures of various physically motivated forms. We find that the Gaussian likelihood performs poorly when the noise distribution deviates from the Gaussian case e.g. heteroscedastic radiometric or heavy-tailed noise. For these non-Gaussian noise structures, we show that the generalised normal likelihood is on a similar Bayesian evidence scale with comparable sky-averaged 21-cm signal recovery as the ground truth likelihood function of our injected noise. We therefore propose the generalised normal likelihood function as a good approximation of the true likelihood function if the noise structure is a priori unknown.
