利用基于仿真的推断探索21厘米功率谱的似然性
Exploring the likelihood of the 21-cm power spectrum with simulation-based inference
AI总结：
本文通过基于仿真的推断研究宇宙21厘米功率谱似然的常见近似影响，发现高斯混合神经密度估计器能以更少仿真获得准确且无偏的后验。
摘要：
对宇宙21厘米功率谱（PS）的观测正开始使我们在宇宙最初的十亿年里，能够对星系性质和物理宇宙学进行精确的贝叶斯推断。在此，我们研究了此类推断中所使用的关于似然的常见近似的影响，包括：（i）假设高斯函数形式；（ii）从单次实现中估计均值；以及（iii）在参数空间中的单一点上估计（协）方差。我们将使用显式似然的“经典”推断与基于仿真的推断（SBI）进行比较，后者从训练集中估计似然。我们的前向模型包括：（i）利用21cmFAST通过改变紫外和X射线星系参数以及初始条件计算得到的宇宙21厘米信号实现；（ii）对应于SKA1-Low进行1000小时积分的望远镜噪声实现；（iii）剔除与前景主导的、视界“楔形”区域相对应的傅里叶模式。我们发现，一维功率谱似然可以用考虑波模和红移区间之间协方差的高斯分布很好地描述（高阶相关性很小）。然而，从随机实现或在参数空间中的单一点上估计前向模型均值和（协）方差的常见方法会导致有偏且过度约束的后验。我们的最佳结果来自使用SBI以高斯混合神经密度估计器拟合非高斯似然。与经典的显式似然推断相比，这种SBI可以用少一个数量级的仿真来完成。因此，SBI以相对较低的计算成本提供了准确的后验。
英文摘要：
Observations of the cosmic 21-cm power spectrum (PS) are starting to enable precision Bayesian inference of galaxy properties and physical cosmology, during the first billion years of our Universe. Here we investigate the impact of common approximations about the likelihood used in such inferences, including: (i) assuming a Gaussian functional form; (ii) estimating the mean from a single realization; and (iii) estimating the (co)variance at a single point in parameter space. We compare "classical" inference that uses an explicit likelihood with simulation based inference (SBI) that estimates the likelihood from a training set. Our forward-models include: (i) realizations of the cosmic 21-cm signal computed with 21cmFAST by varying UV and X-ray galaxy parameters together with the initial conditions; (ii) realizations of the telescope noise corresponding to a 1000 h integration with SKA1-Low; (iii) the excision of Fourier modes corresponding to a foreground-dominated, horizon "wedge". We find that the 1D PS likelihood is well described by a Gaussian accounting for covariances between wavemodes and redshift bins (higher order correlations are small). However, common approaches of estimating the forward-modeled mean and (co)variance from a random realization or at a single point in parameter space result in biased and over-constrained posteriors. Our best results come from using SBI to fit a non-Gaussian likelihood with a Gaussian mixture neural density estimator. Such SBI can be performed with up to an order of magnitude fewer simulations than classical, explicit likelihood inference. Thus SBI provides accurate posteriors at a comparably low computational cost.
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