利用稀疏网格进行有效的宇宙学参数采样
Efficient cosmological parameter sampling using sparse grids
摘要：
我们提出了一种新的方法，显着加快宇宙学参数采样。该方法依赖于构造一个插值的CMB对数似然稀疏网格的基础上，这是作为一个快捷的似然评估。我们在参数空间中的一个大区域内获得了优异的结果，包括约25个对数似然峰周围，我们几乎完美地再现了一维投影的可能性。在速度和精度方面，我们的技术与现有的基于多项式插值或神经网络的参数估计加速方法相比具有竞争力，同时具有一定的优势。在我们的方法中，没有产生非物理摆动的危险，因为它可以是高次多项式拟合的情况。此外，我们不需要像神经网络那样长的训练时间，但是插值的构造由评估采样点处的似然性所花费的时间来确定，这可以并行到任意程度。我们的方法是完全通用的，它可以自适应地利用底层函数的属性。因此，我们可以将其应用于任何需要精确插值函数的问题。
英文摘要：
We present a novel method to significantly speed up cosmological parameter sampling. The method relies on constructing an interpolation of the CMB-log-likelihood based on sparse grids, which is used as a shortcut for the likelihood-evaluation. We obtain excellent results over a large region in parameter space, comprising about 25 log-likelihoods around the peak, and we reproduce the one-dimensional projections of the likelihood almost perfectly. In speed and accuracy, our technique is competitive to existing approaches to accelerate parameter estimation based on polynomial interpolation or neural networks, while having some advantages over them. In our method, there is no danger of creating unphysical wiggles as it can be the case for polynomial fits of a high degree. Furthermore, we do not require a long training time as for neural networks, but the construction of the interpolation is determined by the time it takes to evaluate the likelihood at the sampling points, which can be parallelised to an arbitrary degree. Our approach is completely general, and it can adaptively exploit the properties of the underlying function. We can thus apply it to any problem where an accurate interpolation of a function is needed.
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