We advocate for a new paradigm of cosmological likelihood-based inference,
leveraging recent developments in machine learning and its underlying
technology, to accelerate Bayesian inference in high-dimensional settings.
Specifically, we combine (i) emulation, where a machine learning model is
trained to mimic cosmological observables, e.g. CosmoPower-JAX; (ii)
differentiable and probabilistic programming, e.g. JAX and NumPyro,
respectively; (iii) scalable Markov chain Monte Carlo (MCMC) sampling
techniques that exploit gradients, e.g. Hamiltonian Monte Carlo; and (iv)
decoupled and scalable Bayesian model selection techniques that compute the
Bayesian evidence purely from posterior samples, e.g. the learned harmonic mean
implemented in harmonic. This paradigm allows us to carry out a complete
Bayesian analysis, including both parameter estimation and model selection, in
a fraction of the time of traditional approaches. First, we demonstrate the
application of this paradigm on a simulated cosmic shear analysis for a Stage
IV survey in 37- and 39-dimensional parameter spaces, comparing $\Lambda$CDM
and a dynamical dark energy model ($w_0w_a$CDM). We recover posterior contours
and evidence estimates that are in excellent agreement with those computed by
the traditional nested sampling approach while reducing the computational cost
from 8 months on 48 CPU cores to 2 days on 12 GPUs. Second, we consider a joint
analysis between three simulated next-generation surveys, each performing a
3x2pt analysis, resulting in 157- and 159-dimensional parameter spaces.
Standard nested sampling techniques are simply not feasible in this
high-dimensional setting, requiring a projected 12 years of compute time on 48
CPU cores; on the other hand, the proposed approach only requires 8 days of
compute time on 24 GPUs. All packages used in our analyses are publicly
available.

我们倡导一种新的宇宙学基于概率的推断范式，利用最近在机器学习及其底层技术中的发展，加速在高维环境中的贝叶斯推断。具体来说，我们结合了（i）模拟 —— 其中训练一个机器学习模型来模仿宇宙观测量，例如 CosmoPower-JAX；（ii）可导性和概率编程，例如 JAX 和 NumPyro；（iii）可伸缩的 MCMC 采样技术，可以利用梯度，例如哈密顿蒙特卡罗；以及（iv）解耦且可伸缩的贝叶斯模型选择技术，纯粹从后验样本计算贝叶斯证据，例如在 harmonic 中学到的调和均值。这一范式使我们能够在传统方法的一小部分时间内进行完整的贝叶斯分析，包括参数估计和模型选择。首先，我们在 37 - 维和 39 - 维参数空间中，通过模拟的宇宙剪切分析，展示了这种范式的应用，比较了 ΛCDM 模型和动力学暗能量模型（$w_0w_a$CDM）。我们的结果与传统的嵌套采样方法计算得到的后验轮廓和证据估计非常吻合，而且计算成本从需要 48 个 CPU 核心上的 8 个月时间减少到了使用 12 个 GPU 的 2 天时间。其次，我们考虑了三个模拟的下一代调查的联合分析，每个调查都进行了 3x2pt 分析，得到了 157 - 维和 159 - 维参数空间。在这种高维环境中，标准的嵌套采样技术根本不可行，需要在 48 个 CPU 核心上投入 12 年的计算时间。而另一方面，我们提出的方法只需要 24 个 GPU 的 8 天计算时间。我们在分析中使用的所有软件包都是公开可用的。